Limits Continuity And Differentiability

Let

$$\begin{aligned} f(x) & =x+a \sqrt{2} \sin x & & , 0 \leq x<\frac{\pi}{4} \\ & =2 x \cot x+b & & \frac{\pi}{4} \leq x<\frac{\pi}{2} \\ & =a \cos 2 x-b \sin x & & \frac{\pi}{2} \leq x \leq \pi \end{aligned}$$

If \(\mathrm{f}(\mathrm{x})\) is continuous for \(0 \leq \mathrm{x} \leq \pi\), then