If for non-zero distinct real numbers a, b and c, f(x)= {x α+√ 2 a sin x, 0 ≤ x<(π)/4; 2 x α cot x-c sin 2 x, (π)/4 ≤ x<(π)/2; -8 a c cos 2 x-π α b,…

If for non-zero distinct real numbers $\displaystyle a, b$ and $\displaystyle c$, $$f(x)= \begin{cases}x \alpha+\sqrt{2} a \sin x, & 0 \leq x<\frac{\pi}{4} \\ 2 x \alpha \cot x-c \sin 2 x, & \frac{\pi}{4} \leq x<\frac{\pi}{2} \\ -8 a c \cos 2 x-\pi \alpha b, & \frac{\pi}{2} \leq x \leq \pi\end{cases} $$ is continuous on $\displaystyle [0, \pi]$, then