Find the maximum value $a$ of the function $f ( x ) = 2 \cos \left( x - \frac { \pi } { 3 } \right) + 2 \sqrt { 3 } \sin x$. Find the value of $a ^ { 2 }$. [3 points]
Find the maximum value $a$ of the function $f ( x ) = 2 \cos \left( x - \frac { \pi } { 3 } \right) + 2 \sqrt { 3 } \sin x$. Find the value of $a ^ { 2 }$. [3 points]