Suppose we have a rectangle at the center of the coordinates. One top point of the rectangle has the coordinates (a, b), the second (-a, b), third (-a, -b) and (a, -b). We rotate this rectangle with the angle $\phi $ counterclockwise to get a second rectangle.
Question: Find the common area of these two rectangles.
By common area I mean the area of the polygon that is limited by the intersection points of the two rectangles