Use Various Trigonometric Identities to Simplify the Expression Then Integrate $$\int \cos ^ { 6 } \theta \sin 2 \theta d \theta$$

Multiple Choice

Use various trigonometric identities to simplify the expression then integrate.
- $$\int \cos ^ { 6 } \theta \sin 2 \theta d \theta$$

A) $- \frac { 1 } { 4 } \cos ^ { 8 } \theta + C$
B) $\frac { 1 } { 8 } \cos ^ { 7 } \theta + C$
C) $- \frac { 2 } { 9 } \cos ^ { 9 } \theta + C$
D) $\frac { 2 } { 7 } \cos ^ { 6 } \theta + C$