\displaystyle =16\int_0^\frac{\pi}{2} \sin t \cos^2 t dt=\left[ \begin{array}{cc} \cos t=s & -\sin t dt=ds \\ 0\rightsquigarrow 1 & \frac{\pi}{2} \rightsquigarrow 0 \end{array}\right]=16\int_0^1s^2 ds=\frac{16}{3}