$\displaystyle P= \left \{(x, y) :0 \leq x-y \leq \pi, 0 \leq x+2y \leq \frac{\pi} {2} \right \}$ 이라고 할 때, $\displaystyle \iint _ {P} \sin (x-y) \cos (x+2 y) d x d y$ 의 값은?

• ①$\displaystyle \frac{1} {6}$
• ②$\displaystyle \frac{1} {3}$
• ③$\displaystyle \frac{1} {2}$
• ④$\displaystyle \frac{2} {3}$