These are the steps you need to follow to stream Rakuten TV content on your Chromecast using an Android device:
Your Chromecast and your Android device must be connected to the same WiFi network. Once this is done, the "Chromecast" button will appear as you can see it in the picture below.
When you click on the Chromecast button, you will see a list of the available Chromecasts; just choose yours.
Your Android device's Rakuten TV app and your Chromecast will connect and the Chromecast symbol will turn green.
Once you enter the detail page of any movie, you'll have the option to stream it on Chromecast by tapping the green symbol. Just choose the playback option you wish.
If you have followed these steps and the "Chromecast" button isn't available yet, follow the additional instructions here.