A horizontal park is in the shape of a triangle $O A B$ with $A B = 16$. A vertical lamp post $O P$ is erected at the point $O$ such that $\angle P A O = \angle P B O = 15 ^ { \circ }$ and $\angle P C O = 45 ^ { \circ }$, where $C$ is the midpoint of $A B$. Then $( O P ) ^ { 2 }$ is equal to (1) $\frac { 32 } { \sqrt { 3 } } ( \sqrt { 3 } - 1 )$ (2) $\frac { 32 } { \sqrt { 3 } } ( 2 - \sqrt { 3 } )$ (3) $\frac { 16 } { \sqrt { 3 } } ( \sqrt { 3 } - 1 )$ (4) $\frac { 16 } { \sqrt { 3 } } ( 2 - \sqrt { 3 } )$
A horizontal park is in the shape of a triangle $O A B$ with $A B = 16$. A vertical lamp post $O P$ is erected at the point $O$ such that $\angle P A O = \angle P B O = 15 ^ { \circ }$ and $\angle P C O = 45 ^ { \circ }$, where $C$ is the midpoint of $A B$. Then $( O P ) ^ { 2 }$ is equal to\\
(1) $\frac { 32 } { \sqrt { 3 } } ( \sqrt { 3 } - 1 )$\\
(2) $\frac { 32 } { \sqrt { 3 } } ( 2 - \sqrt { 3 } )$\\
(3) $\frac { 16 } { \sqrt { 3 } } ( \sqrt { 3 } - 1 )$\\
(4) $\frac { 16 } { \sqrt { 3 } } ( 2 - \sqrt { 3 } )$