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