24" Cinema Display connected to Apple TV box. Is it possible?

Hey,

I recently purchased an old 24" Cinema Display, which I am super happy with. It works great as an extra screen for my Macbook Pro (2012). My idea is to also use the Display as a TV, connected wirelessly to my Macbook... To do this I was hoping to station my Apple TV box (3rd Gen) with the Display, and connect the Macbook to the Display via Apple TV wirelessly. My question is..would this work?

I am thinking that I need either a male HDMI>female MiniDisplay? or a female HDMI/female MiniDisplay (does this even exist?) but I am not having much luck searching.

Any recommendations would be greatly appreciated!

Thanks,

Thomas