Assuming a>0 the equation is a pshwre with radius . We pass a plane through it meaning half the length of the radius, see below.
So know that and now we need the bounds on . That means we need to find the red angle.
This can be done with some geometry. I drew a red line to show the triangle. Notice we get a small right triangle inside. The hypotenuse is twice as long as one of its sides, this is a triangle. So the red angle is .