JEE Math Practice Question
Let $f:[0,2] \rightarrow \mathbb{R}$ 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 $\alpha, \beta \in[0,2]$ are such that $\{x \in[0,2]: f(x) \geq 0\}=[\alpha, \beta]$, then what is the value of $\beta-\alpha$?
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