Spherical coordinates, angle question

[gr3g1]

Hey guys,
Im trying to figure out how the angles for the following sphere are obtained.


x^{2} + y^{2} + z^{2} = 4, y = x, y = \sqrt[]{3}x, z = 0


I understand that the integral is:

\int_{0}^{\pi/2}\int_{\pi/4}^{?}\int_{0}^{2}

However, I can't not see how the "?" interval is found! I know it is using y = sqrt(3)*x
pi/4 was determined because 90/2 = 45 degrees.

Thanks in advance

 

[Billy Bob]

Look at the xy plane from "above," and draw the region bounded by y=x, y=sqrt(3)*x, and the circle of radius 2 centered at origin. Where are the intersection points? Any famous angles?