Calculus Question

This is pretty in-your-face, from where I sat at least. I had a test today in my Calculus class, and I did pretty good... except for this question, which haunted me for the entire 80 minutes.

Find the critical numbers, establish whether it is increasing or decreasing at intervals between critical numbers, the points of inflection, at what intervals it is concave upward and concave downward, and establish whether each extrema is a minimum or maximum using the first and second derivative tests.

Okay, not too bad... but the equation itself was so obnoxious I couldn't even find the critical numbers! Maybe my approach was just wrong..

f(x)=2sin(x)+sin(2x)
so
f'(x)=2cos(x)+2cos(2x) (right?)
and to find critical numbers, you set the derivative equal to zero:
0=2cos(x)+2cos(2x)
The problem's obviously the 2x. Am I stupid? How do you solve this?