Chapter 14.7, Problem 8E

To determine

To calculate: The value of the provided triple iterated integral ${\displaystyle {\int }_0^{\frac{\pi }{4}}{\displaystyle {\int }_0^{\frac{\pi }{4}}{\displaystyle {\int }_0^{\cos \theta }{\rho }^2\sin \varphi \cos \varphi d\rho d\theta d\varphi }}}$