Show that

$$\cos \theta \left(9\tan \theta +\frac{4}{\tan \theta }\right)\equiv 5\sin \theta +\frac{4}{\sin \theta }$$

for $\theta \ne \frac{n\pi }{2}$, where $n$ is an integer.

Hence solve, for $0<x<2\pi$, the equation

$$\cos x\left(9\tan x+\frac{4}{\tan x}\right)=12\sin x-2$$

giving your answers to 3 significant figures.