Let \( f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R \) be defined as \(f(x)=\left\{\begin{array}{ccc}(1+|\…

Let \( f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R \) be defined as

\(f(x)=\left\{\begin{array}{ccc}(1+|\sin x|)^{\frac{3 a} {|\sin x|}} & , & -\frac{\pi}{4}<x<0 \\b & , & x=0 \\e^{\frac{\cot 4 x} { \cot 2 x}} & , & 0<x<\frac{\pi}{4}\end{array}\right.\)

If \( f \) is continuous at \( x=0 \), then the value of \( 6 a+b^{2} \) is equal to

[JEE Main 2021, 27 Jul (Shift 1)]