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 ABQCDP to the remaining area of ABCD?

A

$$4 + \frac{(\sqrt{\ 2})}{3}$$

B

2($$\sqrt{\ 3}$$) - 1

C

2 + ($$\sqrt{\ 3}$$)

D

$$\frac{(10 - 3(\sqrt{\ 3})}{9}$$