So The original function was
$$f(x) = 2\sin t-\cos 2t$$ on interval $[0,2\pi]$.
Now I took the derivative which was
$$f'(x) = 2(\cos t+\sin2t)$$
Now I set it equal to zero but I am stuck not knowing how to proceed to find the critical points:
$$\cos t + \sin 2t = 0$$ (since $2$ cannot equal $0$)
So what do I do now?