$\displaystyle \int _ {\frac{1} {2}} ^ {1} \int _ {\sqrt{1-x^ {2}}} ^ {\sqrt{3} x} \arctan \frac{y} {x} d y d x+ \int _ {1} ^ {2} \int _ {0} ^ {\sqrt{4-x^ {2}}} \arctan \frac{y} {x} d y d x$ 의 값은?

• ①$1$
• ②$\displaystyle \frac{\pi} {2}$
• ③$\displaystyle \frac{\pi ^ {2}} {9}$
• ④$\displaystyle \frac{\pi ^ {2}} {12}$