where is the measure of the angle from the positive z axis and is the plane angle.
Alot of calculus books reverse the two angles.
First note that you will want to use spherical coordinates setting the equations equal gives
plugging this into either equation gives
So the circle of intersection of the two objects is described above
Using the above information we can find the angle from the positive z-axis to be
So the radius and the plane angle needs to sweep out the whole circles so it goes from