The Entity.Orientation quaternion and Entity.OrientationMatrix 3x3 matrix both provide the current orientation and can be used to orient a camera. If you want Euler angles, then you'll need to convert orientation to Euler angles using the desired convention (there is no built-in helper for this since there are many different possible conventions). On the other hand, I would suggest running away from Euler angles as fast as you can; working with the transforms directly turns out to be a lot easier with any nontrivial transform.
Also, if you want to make a camera look at an entity as opposed to using the entity's orientation directly, the XNA Matrix.CreateLookAt method would do the trick.