For $x \in \left(0, \pi \right),$ the equation $\sin x+2\sin 2x-\sin 3x=3$ has

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

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

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