Finding asymptotes+Fundamental identities

Hey, I'm new to calculus, and I can't figure out this problem.(Headbang)

You start with:

y = TAN (2 SIN x) -pi __<__ x __<__ pi

Since: TAN x = (SIN x / COS x),

you can get

y= SIN (2 SIN x) / COS (2 SIN x)

Then, since the asymptote is where the equation is undefined (or equals infinity), we need to find the value of x which causes the denominator to equal 0.

COS (2 SIN x) = 0

The cosine of __+__pi/2 is 0, so

2 SIN x = __+__pi/2

SIN x = __+__pi/4

x = __+__ SIN^-1 pi/4

The problem is that there are two answers, but I can't figure out how to work out the next one, which the book says is

x = __+__ (pi - SIN^-1[pi/4]

Help, plz!

I'd also like a way to type in a pi symbol, if that's possible.(Thinking)