2013 AMC 12B Problem 20

For 135^\circ < x < 180^\circ, points P=(\cos x, \cos^2 x), Q=(\cot x, \cot^2 x), R=(\sin x, \sin^2 x) and S =(\tan x, \tan^2 x) are the vertices of a trapezoid. What is \sin(2x)?

\textbf{(A)}\ 2-2\sqrt{2}\qquad\textbf{(B)} 3\sqrt{3}-6\qquad\textbf{(C)}\ 3\sqrt{2}-5\qquad\textbf{(D)}\ -\frac{3}{4}\qquad\textbf{(E)}\ 1-\sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.