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Ta có:
$2\tan(2x+\frac{\pi}{4})-\cot(\frac{\pi}{4}-2x)=\sqrt3$
$\Leftrightarrow 2\tan(2x+\frac{\pi}{4})-\tan(2x+\frac{\pi}{4})=\sqrt3$
$\Leftrightarrow \tan(2x+\frac{\pi}{4})=\sqrt3$
$\Leftrightarrow 2x+\frac{\pi}{4}=\frac{\pi}{3}+k\pi,k\in\mathbb{Z}$
$\Leftrightarrow x=\frac{\pi}{24}+\frac{k\pi}{2},k\in\mathbb{Z}$.
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