Non-Elementary Integration · Medium problem

Wallis' formula for even powers is $\displaystyle\int_0^{\pi/2}\sin^{2n}x\,dx=\dfrac{(2n-1)(2n-3)\cdots1}{(2n)(2n-2)\cdots2}\cdot\dfrac\pi2$. Evaluate $\displaystyle\int_0^{\pi/2}\sin^6x\,dx$.