There are plenty of code snippets you can google for computing euler angles from a quaternion or matrix. You have to decide for yourself how to handle gimbal lock at the poles.
Saying just "Euler" is super ambiguous. Anyway, you can have a look at OVR_Math.h and especially Quat::GetEulerAngles and Matrix4::ToEulerAngles.
The difference with Unity is that the native API doesn't assume it knows your coordinate system, so you will probably have to work a little more to make sure you get what you want. There are a lot of ways to describe rotations.