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