How do I algebraically determine how many solutions a trigonometric solution have $0\leq x\leq 2\pi$? So far I have been drawing graphs for each question and counted the solutions but I want a way to do this algebraically. Many people tell me to use the double angle identities but I haven't learned it yet. I know that the period of $\sin$ and $\cos$ are $2\pi$ and $\tan$ is $\pi$. One of the questions on my test was like..

Determine how many solutions do the following equations have for $0\leq x\leq 2\pi$. 

a) $\sin(3x)=-1/4 $

b)$(\tan(2x))^2=1$

Thanks in advance.