Google Music without Root?

Title says it all. Is there any way to use Google Play Music on my fire TV? I at first tried with various "casting" or "mirroring" apps from my Phone, but none of them seem to work. Ive thought about rooting so I could actually install the google services stuff, but I would like to avoid that if possible.

I have the Fire TV 2.

EDIT: And I see this is a no question area... So if a mod could move it to the appropriate area...

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