Find the values of \( a \) and \( b \) so that the function \[ f(x)=\left[\begin{array}{rr} x+...

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Find the values of \( a \) and \( b \) so that the function
\[
f(x)=\left[\begin{array}{rr}
x+a \sqrt{2} \sin x, & 0 \leq x\frac{\pi}{4} \\
2 x \cot x+b, & \frac{\pi}{4} \leq \mathrm{x} \leq \frac{\pi}{2} \\
a \cos 2 x-\sin 2 x & \frac{\pi}{2}x \leq \pi
\end{array}\right.
\]
is continuous in \( [0, \pi] \)
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