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PT
$\Leftrightarrow (\sin x+\cos x) (\sin^{2}x+\cos^{2}x -\sin x\cos x )= (\sin x+\cos x)(\cos x-\sin x)(2\cos x-\sin x)$
$\Leftrightarrow \left[ {\begin{matrix}\sin x+\cos x=0\\1-\sin x\cos x= (\cos x-\sin x)(2\cos x-\sin x) \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix}\sin (x +\dfrac{\pi}{4})=0\\1-\sin x\cos x= 2\cos^2x-3\sin x\cos x+\sin^2x \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix}\sin (x
+\dfrac{\pi}{4})=0\\ \cos^2x-2\sin x\cos x=0
\end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix}\sin (x
+\dfrac{\pi}{4})=0\\ \cos x=0\\\sin x =1/2
\end{matrix}} \right.$
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