For $45^{\circ }<x<90^{\circ }$, 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 $\sin (2x)$?