Let \( f: R \rightarrow R \) be defined as \(f(x)=\left\{\begin{array}{cc}\frac{x^{3}}{(1-\cos 2 x)^{2}} \log _{e}\left(…

Let \( f: R \rightarrow R \) be defined as

\(f(x)=\left\{\begin{array}{cc}\frac{x^{3}}{(1-\cos 2 x)^{2}} \log _{e}\left(\frac{1+2 x e^{-2 x}}{\left(1-x e^{-x}\right)^{2}}\right), & x \neq 0 \\\alpha & , x=0\end{array}\right.\)

If \( f \) is continuous at \( x=0 \), then \( \alpha \) is equal to

[JEE Main 2021, 22 Jul (Shift 2)]