As of now, you can't. It's laughable.. Google is really a very large company without any direction whatsoever. They don't support integration of YT Music and Chromecast Audio.

For now, you'll have to use the Chromecast App sound-transcoding. You can find those instructions here, from your Android device:

1. Connect your Android device to the same Wi-Fi network as your Chromecast Audio.
2. Open the Google Cast app Chromecast cast icon.
3. In the top left corner, tap the navigation drawer More menu icon.
4. Tap the Cast Screen + Audio button.
5. Select your Chromecast Audio.

This has a lot of caveats. The sound is inferior. The device that is doing the screencasting is communicating to Chromecast Audio directly (putting your hand over the antenna and killing the wifi throughput will cause skipping). And, you won't be able to answer a phone call.

As of now, you can't. Google does not support integration of YT Music and Chromecast Audio.

For now, you'll have to use the Chromecast App sound-transcoding. You can find those instructions here, from your Android device:

1. Connect your Android device to the same Wi-Fi network as your Chromecast Audio.
2. Open the Google Cast app Chromecast cast icon.
3. In the top left corner, tap the navigation drawer More menu icon.
4. Tap the Cast Screen + Audio button.
5. Select your Chromecast Audio.

This has a lot of caveats. The sound is inferior. The device that is doing the screencasting is communicating to Chromecast Audio directly (putting your hand over the antenna and killing the wifi throughput will cause skipping). And, you won't be able to answer a phone call.