Thunderbolt / Cinema Display + Apple TV

I’m determined to find a way to connect the Apple TV to my Thunderbolt Display. I already have it hooked up to my Cinema Display from 2002 it works great I watch YouTube Netflix, also I can mirror/extend my MacBook through Airplay so it has multiple functions. Ideally I’d like to have the Apple TV hooked up to both with a hdmi splitter. So far my only attempt was getting a mini display female to female hooking up a hdmi to mini display adapter from the Apple TV and no luck. Next option is a Thunderbolt mini display to hdmi but it’s hard to find.