[tex] \text{The domain}\\D:x\in\left(0,\ \dfrac{\pi}{2}\right)\ \cup\ \left(\dfrac{\pi}{2},\ \pi\right)\\\\3\tan^2x-2=\csc^2x-\cot^2x\\\\3\tan^2x-2=\dfrac{1}{\sin^2x}-\dfrac{\cos^2x}{\sin^2x}\\\\3\tan^2x-2=\dfrac{1-\cos^2x}{\sin^2x}\\\\3\tan^2x-2=\dfrac{\sin^2x}{\sin^2x}\\\\3\tan^2x-2=1\ \ \ \ |+2\\\\3\tan^2x=3\ \ \ \ |:3\\\\\tan^2x=1\Rightarrow\tan x=\pm\sqrt1\\\\\tan x=-1\ \vee\ \tan x=1\\\\x=\dfrac{3\pi}{4}\ \vee\ x=\dfrac{\pi}{4} [/tex]
[tex]\text{Used:}\\\\\csc x=\dfrac{1}{\sin x}\\\\\cot x=\dfrac{\cos x}{\sin x}[/tex]
