Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

A

$$\frac{4 \sqrt 2}{3}$$

B

$$2 + \sqrt{3}$$

C

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

D

$$1+\frac{1}{\sqrt3}$$

E

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