Let $$f:[0, 2]\rightarrow R$$ be the function defined by

$$f(x) = (3- \sin(2\pi x)) \sin \left(\pi x - \frac{\pi}{4}\right) - \sin\left(3\pi x + \frac{\pi}{4}\right)$$

If $$\alpha, \beta \epsilon [0, 2]$$ are such that $$\left\{x \epsilon [0,2] : f(x) \geq 0\right\} = [\alpha, \beta]$$, then the value of $$\beta - \alpha$$ is _________