Functional Equation and Area Bounded

Let $f: R \rightarrow R$ be a function such that $f(x)+3f\left(\dfrac{\pi}{2}-x\right)=\sin x,\; x\in R$. Let maximum value of f on R be α. If the area of the region bounded by the curves $g(x)=x^{2}$ and $h(x)=\beta x^{3}$, β>0, is $\alpha^{2}$, then $30\beta^{3}$ is equal to ______.