Solve the trigonometric equation $\csc^2 \theta= 5 \cot \theta + 7$ Solve the given equation. Let k be any integer. 
$$\csc^2 θ = 5 \cot θ + 7$$
I just need the first step or two please. I tried converting it:
$$\frac{1}{\sin^2 θ} = \frac {5\cosθ}{\sinθ} + 7$$
Then I tried a number of different ways to simplify it but it didn't work out

Notice, $$csc^2\theta=5\cot \theta+7$$ 
$$\cot^2\theta+1=5\cot \theta+7$$ $$\cot^2\theta-5\cot \theta-6=0$$
$$(\cot\theta -6)(\cot\theta+1)=0$$
$$\implies \cot\theta-6=0 \iff \tan \theta=\frac{1}{6}\iff \color{blue}{\theta=n\pi+\tan^{-1}\left(\frac{1}{6}\right)}$$
$$\implies \cot\theta+1=0 \iff \tan \theta=-1=-\tan\frac{\pi}{4} \iff \color{blue}{\theta=n\pi-\frac{\pi}{4}}$$
Where,  $\color{blue}{n}$ is any integer
