Breaking through c3 trig

When I'm solving trig equations I always do this:

1.) Make every term the same. What I mean by this is, if you have $cos2x$, $sinx$ or $tan3x$ you want to make them all the same so in each trig function you just have $x$, $2x$ or $3x$.

2.) Make it terms of only one trig function. So by using identities, make it into one of the sine, cosine or tan functions (Preferably not sec, cosec or cot because they're harder to solve.)

3.) Remember not to cancel trig functions in doing steps 1.) and 2.)! E.g. if you have $sinxcos3x = cosec2xsinx$ or $sinx(1 - tanx) = 0$ it is very tempting to cancel the $sinx$ but DO NOT! They hold extra solutions.

4.) Once you have something in the form $cos(ax) = b$ or something similiar you can solve it by the ACTS quadrant method or by looking at the graph of the trig function.

I was just doing it. thanks though this is like when i was on log i couldn't do it for ages and wasn't able to see what everyone esle was seeing. also shouldnt that be $sin\frac{1}{2}\theta=\frac{3}{2 \sqrt{3}}$

They're the same.

Also, to solve it, you'll need some sort of range in which $\theta$ lies in. Other than that, you just solve it as usual, with your acute angle, CAST diagrams, or whatever way you usually work them out.