Find the Exact Value of the Given Expression $\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)$

Multiple Choice

Find the exact value of the given expression. $\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)$

A) $\frac { 1 - \sqrt { 3 } } { 2 \sqrt { 2 } }$
B) $\frac { 1 + \sqrt { 3 } } { 2 \sqrt { 2 } }$
C) $\frac { - 1 - \sqrt { 3 } } { 2 \sqrt { 2 } }$
D) $\frac { - 1 + \sqrt { 3 } } { 2 \sqrt { 2 } }$