Let f: R → R be a function defined by f(x)=4^x/(4^x+2) and M=∫_f(a)^f(1-a) x sin^4(x(1-x)) d x, N=∫_f(a)^f(1-a) sin^4(x(1-x)) d x; a ≠ 1/2. If α M=β…

Let $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $\displaystyle f(x)=\frac{4^x}{4^x+2}$ and $$M=\int_{f(a)}^{f(1-a)} x \sin ^4(x(1-x)) d x, N=\int_{f(a)}^{f(1-a)} \sin ^4(x(1-x)) d x ; a \neq \frac{1}{2} \text {. If } $$ $\displaystyle \alpha M=\beta N, \alpha, \beta \in \mathbb{N}$, then the least value of $\displaystyle \alpha^2+\beta^2$ is equal to $\displaystyle \_\_\_\_$