이중적분 $\displaystyle \iint _ {R} \tan ^ {-1} \left (\frac{y} {x} \right) d A$ 의 값은?

(단, $R= \left \{(x, y) \vert 1 \leq x ^ {2} +y ^ {2} \leq 4, 0 \leq y \leq x \right \}$)

• ①$\displaystyle \frac{3} {64} \pi ^ {2}$
• ②$\displaystyle \frac{5} {64} \pi ^ {2}$
• ③$\displaystyle \frac{7} {64} \pi ^ {2}$
• ④$\displaystyle \frac{9} {64} \pi ^ {2}$
• ⑤$\displaystyle \frac{11} {64} \pi ^ {2}$