Find the extrema of a trigonometric function

I am to find the extrema of the following function. f(x) = 2 sin x + cos 2x when 0 __<__ x __<__ 2pi. taking the derivative of the function I come up with 2 cos x -2 sin 2x. At this point I need to find the extrema on the interval 0 __<__ x __<__ 2pi. I think the solution is to evaluate 2 cos x = 0. being cos x = -2 and then, -2 sin 2x = 0. that being sin x = 2/2 = sin 1, being pi/2. OR, am I to use the double angle identity in the function and change the derivative of 2 cos x to, 1- 2sin^2 x - 2 sin 2x = 0. I am confused at this point. Can someone please help?