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PT
$\Leftrightarrow (1-\sin^{2}x)\tan x+(1-\cos^{2}x)\cot x +1+\sin 2x = 0$
$\Leftrightarrow \cos^2 x\tan x+\sin^2 x\cot x +1+\sin 2x = 0$
$\Leftrightarrow \cos x\sin x+\sin x\cos x +1+\sin 2x = 0$
$\Leftrightarrow 2\cos x\sin x +1+\sin 2x = 0$
$\Leftrightarrow 1+2\sin 2x = 0$
$\Leftrightarrow \sin 2x = -1/2$.
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