Find the Exact Value of the Given Expression $\cos \left( 120 ^ { \circ } + 315 ^ { \circ } \right)$

Multiple Choice

Find the exact value of the given expression. $\cos \left( 120 ^ { \circ } + 315 ^ { \circ } \right)$

A) $\frac { ( 1 - \sqrt { 3 } ) ( 2 \sqrt { 2 } ) } { 8 }$
B) $\frac { ( - 1 + \sqrt { 3 } ) ( 2 \sqrt { 2 } ) } { 8 }$
C) $\frac { ( 1 + \sqrt { 3 } ) ( 2 \sqrt { 2 } ) } { 8 }$
D) $\frac { ( - 1 - \sqrt { 3 } ) ( 2 \sqrt { 2 } ) } { 8 }$