Let \( f:[0,2] \rightarrow R \) be the function defined by \[ f(x)=(3-\sin (2 \pi x)) \sin \left...

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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 \( \alpha, \beta \in[0,2] \) are such that \( \{\mathrm{x} \in[0,2] ; f(x) \geq 0\}=[\alpha, \beta] \), then the value of \( \beta-\alpha \) is
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