$$\max_{0 \leq x \leq \pi} \left\{x - 2\sin x \cos x + \frac{1}{3}\sin 3x\right\} =$$

A

$$\frac{\pi + 2 - 3\sqrt{3}}{6}$$

B

$$\pi$$

C

$$0$$

D

$$\frac{5\pi + 2 + 3\sqrt{3}}{6}$$