$\displaystyle \lim _ {x \rightarrow \infty} \left \{x^ {2} -x^ {2} {\sin} \left (\frac{\pi (1+x)} {2 x} \right) \right \}$ 의 값은?

• ①$0$
• ②$\displaystyle \frac{\pi ^ {2}} {8}$
• ③$\displaystyle \frac{\pi ^ {2}} {4}$
• ④$\displaystyle \frac{\pi ^ {2}} {2}$