$\displaystyle \sin \left (2 \cos ^ {- 1} \left (\frac{\sqrt {2}} {2} \right) \right) + \tan \left (\sin ^ {- 1} \left (\frac{\sqrt {3}} {2} \right) \right)$ 의 값은?

• ①$2 + \sqrt {2}$
• ②$1 + \sqrt {3}$
• ③$\displaystyle \frac{1} {\sqrt {2}} + \frac{1} {\sqrt {3}}$
• ④$\sqrt {2} + \sqrt {3}$