Use Various Trigonometric Identities to Simplify the Expression Then Integrate $$\int \sin \theta \cos \theta \cos 4 \theta d \theta$$

Multiple Choice

Use various trigonometric identities to simplify the expression then integrate.
- $$\int \sin \theta \cos \theta \cos 4 \theta d \theta$$

A) $\frac { 1 } { 6 } \cos 6 \theta + C$
B) $\frac { 1 } { 8 } \cos 2 \theta - \frac { 1 } { 24 } \cos 6 \theta + C$
C) $\frac { 1 } { 24 } \cos 4 \theta + C$
D) $\frac { 1 } { 4 } \cos 2 \theta - \frac { 1 } { 8 } \cos 6 \theta + C$