Question

Cos(2θ) = 5 sin(θ) − 2

Answer 1

Cos(2$cos2 \alpha = 1-sin^{2} \alpha$. 

so...

$1-sin^2\alpha = 5sin\alpha -2 sin^2\alpha + 5sin\alpha -3 = 0$

Is that what you are trying to do? Find the zeros?