This app was mentioned in 7 comments, with an average of 1.43 upvotes
There is Mirroring360 sender (audio requires root)
https://play.google.com/store/apps/details?id=com.splashtop.m360.tx
I haven't been able to get sound to work on my rooted nexus7(marshmallow) to the atv4. Koush's mirror beta app doesn't do audio. However, you maybe able to achieve what you want with localcast on Android using the share button from within other apps. The ATV3 works better with Android because the older airplay protocol. Other apps worth looking at that are Allstream and Airaudio they require root but are amazing for audio. These apps are like rogue amoeba's airfoil but on android, multizone synced airplay. Let me know what you are trying to stream. I may be able to give more suggestions other than mirroring.
Yes mirroring from android to Apple TV is possible: Mirroring360 sender (root needed), some DRM protected content won't mirror. Amazon prime works for mirroring using mirroring360.
My house has a very mixed ecosystem Some of the other apps i've used in my house are: Localcast, web video caster, server cast, toastercast, playto, ezcast, tubio, Allcast, allstream, airaudio, flipps
Edit: fixed mirroring360 sender's name here is the link
https://play.google.com/store/apps/details?id=com.splashtop.m360.tx
I've used mirroring 360 back in the day for mirroring.. Not sure how well it still works. https://play.google.com/store/apps/details?id=com.splashtop.m360.tx
If you mean as a remote, I'm not aware of any other app that does this.
If your Android phone is rooted and has the power try mirroring360 Sender https://play.google.com/store/apps/details?id=com.splashtop.m360.tx&hl=en
Had a look, found 2 apps that seem to be able to do this:
If you don't have root I think you're out of luck (unless you don't need sound), and if so it's probably worth getting a Chromecast.
If you bought it. It may still be in your apps library ( Apps>your apps library). Try not to search for it. Just scroll through.
Another app worth trying if you have root on an android is splashtop's mirroring360. Supports AirPlay iOS too. I've been pretty impressed with it on my Nexus 7 2013. BTW Android Miracasts works really well on FireTV2.
Receiver for fire TV http://www.amazon.com/Splashtop-Inc-Mirroring360-AirPlay-Receiver/dp/B00OLMZIZK
Android https://play.google.com/store/apps/details?id=com.splashtop.m360.tx&hl=en
ChromeOS https://chrome.google.com/webstore/detail/mirroring360-sender/iaigceaehdihlnolehbapjfbbfpnlngg?hl=en
Windows and OSX http://www.mirroring360.com