ĐK: $x\ne \dfrac{\pi}{2}+k\pi$
$\tan x=\tan\dfrac{3\pi}{11}$
$\Leftrightarrow x=\dfrac{3\pi}{11}+k\pi$
$\dfrac{\pi}{4}<x<2\pi$
$\Leftrightarrow \dfrac{\pi}{4}<\dfrac{3\pi}{11}+k\pi<2\pi$
$\Leftrightarrow -0,02<k<1,72$
$\Rightarrow k\in\{0;1\}$
Vậy có 2 nghiệm.