Solve the following for $-2\pi \le \theta \le 2\pi$: $$12\cos(2\theta) – 6 = \sin\theta$$
What I did was used trig identities to make cosine into sine by using $\cos^2\theta = 1 - sin^2(\theta)$ and solving from there. I ended up getting $\theta = -49°$ and $\theta=42°$. However, when it comes to the range, when you go into the negatives, does the CAST rule become reversed? If you could please help me solve this, it would be greatly appreciated!