Let f: R → R be a function such that f(x)+3 f((π)/2-x)= sin x, x ∈ R. Let the maximum value of f on R be α. If the area of the region bounded by the…

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