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 the value of $\beta - \alpha$ is $\_\_\_\_$