2007 AIME I Problem 12

In isosceles triangle A B C, A is located at the origin and B is located at (20,0). Point C is in the first quadrant with A C=B C and \angle B A C=75^{\circ}. If \triangle A B C is rotated counterclockwise about point A until the image of C lies on the positive y-axis, the area of the region common to the original triangle and the rotated triangle is in the form p \sqrt{2}+q \sqrt{3}+r \sqrt{6}+s where p, q, r, s are integers. Find (p-q+r-s) / 2.