Consider a square ABCD with midpoints E, F, G and H of sides AB, BC, CD and DA. Let L denote the line passing through F and H. Consider points P and Q on the line L inside the square such that the angles APD and BQC are both equal 120 degrees. What is the ratio of area ABCQPD (i.e. area of hexagon A-B-C-Q-P-D) to the remaining area of ABCD?