AirPlay not connecting iPhone 5S to Apple TV 2
I have an iPhone 5S with iOS 8.2 and an AppleTV 2 with software version 7.1, but when I bring up the Control Center on the iPhone, tap on AirPlay > AppleTV with mirroring > Done, the screen freezes for a few seconds and then Control Center goes away, but AirPlay isn't connected and there's no change to the AppleTV. If I try to turn on AirPlay without mirroring, it connects, but any music I play won't come out of the TV and the AppleTV's home screen shows no signs that music is being streamed. I've tried rebooting the iPhone, the AppleTV, and my router, but nothing changes. Anyone have any idea what the problem is?
iPhone 5s, iOS 8.2, AppleTV 2 software version 7.1