In isosceles triangle \(ABC\), \(A\) is located at the origin and \(B\) is located at (20,0). Point \(C\) is in the first quadrant with \(AC = BC\) and angle \(BAC = 75^{\circ}\). If triangle \(ABC\) 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 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 \((p-q+r-s)/2\).
(第二十五届AIME1 2007 第12题)