解决方法如下：

1. 首先，您需要设置Android Things项目并添加Google Calendar API到您的项目中。您可以按照谷歌的文档指导来进行设置和添加。

2. 在Android Things项目中，您需要使用Google API客户端库来连接和使用Google Calendar API。您可以在项目的build.gradle文件中添加以下依赖项来引入Google API客户端库：

implementation 'com.google.android.gms:play-services-calendar:17.0.0'

3. 在您的Android Things项目中，您可以创建一个CalendarClient类来处理与Google Calendar API的交互。在这个类中，您可以使用Google API客户端库提供的类和方法来实现与Google Calendar的连接和操作。以下是一个示例的CalendarClient类的代码：

import com.google.android.gms.auth.api.signin.GoogleSignIn;
import com.google.android.gms.auth.api.signin.GoogleSignInAccount;
import com.google.android.gms.auth.api.signin.GoogleSignInOptions;
import com.google.android.gms.common.api.GoogleApiClient;
import com.google.api.client.extensions.android.http.AndroidHttp;
import com.google.api.client.googleapis.auth.oauth2.GoogleCredential;
import com.google.api.client.googleapis.extensions.android.gms.auth.GoogleAccountCredential;
import com.google.api.client.json.JsonFactory;
import com.google.api.client.json.jackson2.JacksonFactory;
import com.google.api.services.calendar.Calendar;
import com.google.api.services.calendar.CalendarScopes;
import com.google.api.services.calendar.model.Event;
import com.google.api.services.calendar.model.Events;

import java.io.IOException;
import java.util.Collections;
import java.util.List;

public class CalendarClient {

    private static final String APPLICATION_NAME = "Your Application Name";
    private static final JsonFactory JSON_FACTORY = JacksonFactory.getDefaultInstance();

    private GoogleAccountCredential credential;
    private Calendar calendarService;

    public CalendarClient() {
        credential = GoogleAccountCredential.usingOAuth2(
                AndroidThingsApp.getInstance(),
                Collections.singleton(CalendarScopes.CALENDAR)
        );
        calendarService = new Calendar.Builder(
                AndroidHttp.newCompatibleTransport(),
                JSON_FACTORY,
                credential
        ).setApplicationName(APPLICATION_NAME).build();
    }

    public void signIn() {
        GoogleSignInOptions signInOptions = new GoogleSignInOptions.Builder(GoogleSignInOptions.DEFAULT_SIGN_IN)
                .requestEmail()
                .requestScopes(new Scope(CalendarScopes.CALENDAR))
                .build();
        GoogleApiClient googleApiClient = new GoogleApiClient.Builder(AndroidThingsApp.getInstance())
                .addApi(Auth.GOOGLE_SIGN_IN_API, signInOptions)
                .build();

        Intent signInIntent = Auth.GoogleSignInApi.getSignInIntent(googleApiClient);
        // Start the sign-in activity
        AndroidThingsApp.getInstance().startActivityForResult(signInIntent, RC_SIGN_IN);
    }

    public void handleSignInResult(Intent data) {
        GoogleSignInResult result = Auth.GoogleSignInApi.getSignInResultFromIntent(data);
        if (result.isSuccess()) {
            GoogleSignInAccount account = result.getSignInAccount();
            if (account != null) {
                credential.setSelectedAccount(account.getAccount());
            }
        } else {
            // Handle sign-in failure
        }
    }

    public List getEvents() throws IOException {
        Events events = calendarService.events().list("primary")
                .setMaxResults(10)
                .setTimeMin(new DateTime(System.currentTimeMillis()))
                .setOrderBy("startTime")
                .setSingleEvents(true)
                .execute();
        return events.getItems();
    }

    public void createEvent(Event event) throws IOException {
        calendarService.events().insert("primary", event).execute();
    }

    public void deleteEvent(String eventId) throws IOException {
        calendarService.events().delete("primary", eventId).execute();
    }
}

4. 在您的Android Things应用程序中，您可以使用CalendarClient类来进行与Google Calendar API的交互。您可以在需要的地方创建一个CalendarClient实例，并调用其方法来完成相应的操作。以下是一个示例的MainActivity类的代码，展示了如何使用CalendarClient来获取日历事件列表：

public class MainActivity extends Activity {

    private CalendarClient calendarClient;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        calendarClient = new CalendarClient();

        // Sign in to Google account
        calendarClient.signIn();

        // Get events
        try {
            List events = calendarClient.getEvents();
            for (Event event : events) {
                // Handle events
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    @Override
    protected void onActivityResult(int requestCode, int resultCode