solving trigonometry equation $20\cot\theta + 15\cot\theta\operatorname{cosec}\theta - 4\operatorname{cosec}\theta = 3(1 + \cot^2 \theta) ?$ how do you solve for $0 < \theta < 360$:
$$20\cot\theta + 15\cot\theta\operatorname{cosec}\theta - 4\operatorname{cosec}\theta = 3(1 + \cot^2 \theta) ?$$
I tried turning the $(1 + \cot^2 \theta)$ part into $\operatorname{cosec}^2$ then dividing through or changing every term into $\sin$ and $\cos$ but I always end up with a dodgy equation that I can't factorise.

Let try to convert the equation to $\sin$ and $\cos$.
$$20\frac{\cos \theta}{\sin\theta}  + 15 \frac{\cos \theta}{\sin\theta}\frac{1}{\sin\theta} - 4\frac{1}{\sin\theta} = 3\frac{1}{\sin^2\theta}$$
$$20\cos\theta\sin\theta + 15\cos\theta-4\sin\theta = 3$$
$$(4\sin\theta+3)(5\cos\theta-1) = 0$$
Now, you can solve the equation.
