For 135^{\circ}<x<180^{\circ}, points P=\left(\cos x, \cos ^{2} x\right), Q=\left(\cot x, \cot ^{2} x\right), R= \left(\sin x, \sin ^{2} x\right), and S=\left(\tan x, \tan ^{2} x\right) are the vertices of a trapezoid. What is \sin (2 x) ?
Answer Choices
A. 2-2 \sqrt{2}
B. 3 \sqrt{3}-6
C. 3 \sqrt{2}-5
D. -\dfrac{3}{4}
E. 1-\sqrt{3}