Definite Integration

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