Let \( f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R \) be defined as
\[
f(x)=\left... VIDEO
Let \( f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R \) be defined as
\[
f(x)=\left\{\begin{array}{ccc}
(1+|\sin x|)^{3 a /|\sin x|} & , & -\frac{\pi}{4}x0 \\
b & , & x=0 \\
e^{\cot 4 x / \cot 2 x} & , & 0x\frac{\pi}{4}
\end{array}\right.
\]
If \( f \) is continuous at \( x=0 \), then the value of \( 6 a+b^{2} \) is equal to
(a) \( 1-e \)
(b) \( e-1 \)
(c) \( 1+e \)
(d) \( e \)
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