Trig Identities and Logs, Solve x within the given interval

Note: I wasn't really sure which board to post this on since this involves both trig identities and logs, but I figured that since Trigonometry generally comes after Algebra that I'd post it in this board. If I put this topic in the wrong board, I apologize for my confusion.

Solve for x in the interval [0, 2 ]:

Now, so far I've tried turning the into and then getting stuck with not knowing how to break down so I can use log identities (subtracting logs with same bases becomes division of factors, for reference). I've also tried breaking it down to the following, but I hit a dead end because it doesn't really seem to lead anywhere that I can tell:

The answer is supposed to be

So, any tips on how to progress, or which way to progress, would be appreciated. Thanks. (Nod)