1. ## Prove trigonometric inequality?

Prove that:
$(\cot^2 x - 1)(3\cot^2 x - 1)(\cot 3x\cdot\tan 2x - 1)\leq -1$
is valid for all values of $x$ for which the LHS is defined.

2. $\cot 3x=\frac{\cot^3x-3\cot x}{3\cot^2x-1}, \ \tan 2x=\frac{2\cot x}{\cot^2x-1}$

The inequality becomes

$-\cot^4x-2\cot^2x-1\leq -1$ and this is true.