You can use Chromecast to play Fiit classes on your TV through an app called iStreamer.
First, you will need Chromecast built into your TV or have a Chromecast dongle connected. Once you have downloaded the iStreamer app from the App Store, you can use the free version to mirror your phone onto your TV:
Make sure both your iPhone/iPad and Chromecast are connected to the same Wi-Fi network and that you have set up a new device on the iStreamer app
Open the iStreamer app
Connect to your TV from the list of available devices
Tap on "Screen Mirror"
Tap on the screen recording button displayed in the app
Tap on "Start Broadcast".
Your iPhone/iPad screen will be mirrored on your TV and you can now start a Fiit class
Below is a video tutorial of this same step by step process:
Paid for solutions are also available and can sometimes be more reliable.