Evaluate the Following Iterated Integral $\int_{0}^{\pi /15}\int_{0}^{\pi/15}\int_{0}^{cos\theta}\rho^{2} \sin \phi \cos \phi d \rho d \theta d \phi$

Multiple Choice

Evaluate the following iterated integral.
$\int_{0}^{\pi /15}\int_{0}^{\pi/15}\int_{0}^{cos\theta}\rho^{2} \sin \phi \cos \phi d \rho d \theta d \phi$

A) $\frac { 1 } { 36 } \left( 5 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 3 } \frac { \pi } { 15 }$
B) $\frac { 1 } { 6 } \left( 5 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 3 } \frac { \pi } { 15 }$
C) $\frac { 1 } { 6 } \left( 3 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 2 } \frac { \pi } { 15 }$
D) $\frac { 1 } { 36 } \left( 5 + \cos \frac { \pi } { 15 } \right) \sin ^ { 3 } \frac { \pi } { 15 }$
E) $\frac { 1 } { 36 } \left( 5 + \cos \frac { 2 \pi } { 15 } \right) \sin ^ { 2 } \frac { \pi } { 15 }$