AMC 12 2013b 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} \textbf{(B)} 3\sqrt{3}-6 \textbf{(C)}\ 3\sqrt{2}-5 \textbf{(D)}\ -\frac{3}{4} \textbf{(E)}\ 1-\sqrt{3}