Disclaimer I am using the spherical coordinates in the following form

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

This gives