Limits Continuity And Differentiability

If the function

$$ f(x)=\left\{\begin{array}{cc} x+a \sqrt{2} \sin x & \text { if } 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+b & \text { if } \frac{\pi}{4} < x \leq \frac{\pi}{2} \\ a \cos 2 x-b \sin x & \text { if } \frac{\pi}{2} < x \leq \pi \end{array}\right. $$

is continuous in $[0, \pi]$ then $a-b=$