OK CeeJay---

If you write this equation down it looks like it may be factorable...

(3sin(theta) - cos(theta))*(sin(theta) + 2cos(theta)) = 0.

Now using the Zero Product Property that means that sin(theta) = cos(theta)/3

and sin(theta) = -2cos(theta).

Now divide both sides of these answers by cos(theta) to get tan(theta) and you have tan(theta)= 1/3 and tan(theta) = -2. Doing the inverses of these gives you your answers...but you have to subtract the second one from 180. These both check.