Use the Given Information to Compute $\cos \left( \frac { \theta } { 2 } \right)$

Multiple Choice

Use the given information to compute $\cos \left( \frac { \theta } { 2 } \right)$ . $\sin \theta = - \frac { 1 } { 8 }$ and $180 ^ { \circ } < \theta < 270 ^ { \circ }$

A) $- \frac { 3 \sqrt { 10 } } { 5 }$
B) $\frac { 3 \sqrt { 6 } } { 14 }$
C) $- \frac { \sqrt { 8 - 3 \sqrt { 7 } } } { 4 }$
D) $- \frac { \sqrt { 5 + 3 \sqrt { 7 } } } { 3 }$
E) $\frac { \sqrt { 5 - 3 \sqrt { 10 } } } { 3 }$