How should I interpret the gyro's information?

I want to make the camera rotate with the gyroscope. (Kind of like Pokemon Go, but for a totally different project) For what I understand, I should use the rotation rate, which is the delta rotation between frames. The problem is setting the initial rotation of the camera so it can match my phones rotation. If I start the app with my phone aiming down, when I lift it so it is looking forward, the camera is looking up, as the "forward" was down when I started the app.

I guess I should use the gravity, but don't know how to transform that information to euler angles.