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

Multiple Choice

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

A) $\frac { 1 } { 12 } \sin 4 \theta - \frac { 1 } { 4 } \sin 6 \theta - \frac { 1 } { 32 } \sin 8 \theta + C$
B) $\frac { 1 } { 12 } \sin 6 \theta - \frac { 1 } { 4 } \sin 4 \theta - \frac { 1 } { 32 } \sin 8 \theta + C$
C) $\frac { 1 } { 12 } \sin 6 \theta - \frac { 1 } { 4 } \sin 8 \theta - \frac { 1 } { 32 } \sin 4 \theta + C$
D) $\frac { 1 } { 2 } \sin 6 \theta - \frac { 1 } { 4 } \sin 4 \theta - \frac { 1 } { 8 } \sin 8 \theta + C$