Let f:(-(π)/4, (π)/4) → R be defined as f(x)= {(1+| sin x|)^((3 a)/(| sin x|)),-(π)/4<x<0; b, x=0; e^cot 4 x / cot 2 x, 0<x<(π)/4} If f is continuous…

Let $\displaystyle f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow \mathbf{R}$ be defined as $$f(x)=\left\{\begin{array}{c} (1+|\sin x|)^{\frac{3 \mathrm{a}}{|\sin x|}},-\frac{\pi}{4}<x<0 \\ \mathrm{~b} \quad, x=0 \\ \mathrm{e}^{\cot 4 x / \cot 2 x} \quad, \quad 0<x<\frac{\pi}{4} \end{array}\right. $$ If $\displaystyle f$ is continuous at $\displaystyle x=0$, then the value of $\displaystyle 6 \mathrm{a}+\mathrm{b}^2$ is equal to :