\( \text { If the function } \) \(f(x)= \begin{cases}(1+|\cos x|)^ \frac{\lambda}{|\cos x|} & , 0<x<\frac{\pi}…

\(
\text { If the function }
\)

\(f(x)= \begin{cases}(1+|\cos x|)^ \frac{\lambda}{|\cos x|} & , 0<x<\frac{\pi}{2} \\ \mu & , \quad x=\frac{\pi}{2} \\ {e^\frac{\cot 6 x}{\cot 4 x}} & \frac{\pi}{2}<x<\pi\end{cases}\)\(\text{ is continuous at  }x=\frac{\pi }{2}\text{, then }9\lambda +6{\log }_{e}\mu +{\mu }^{6}-{e}^{6\lambda }\text{ is equal to }\)

[JEE Main 2023, 25 Jan (Shift 2)]