(of course I forgot all my high school trig...)

The problem states to find the general solution:

$\displaystyle sin^2 (x-30) = sin^2 2x$

I assume since both sides are sin^2, I can just say x-30 = 2x...

x=-30.

That is all I know how to do. But the answer in the book says

x1 = -30+180n

x2 = 10 + 60n

so where does the 10+60n come from and how do I know whether to add 60n or 180n or 360n...?

Thanks