Let f : \(R\to R\) be defined as \(f(x)=\left{\begin{matrix}\frac{{x}^{3}}{{(1−\cos 2x)}^{2}}{\log }_{\text{e}}\left(\fr…

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

\(f(x)=\left{\begin{matrix}\frac{{x}^{3}}{{(1−\cos 2x)}^{2}}{\log }_{\text{e}}\left(\frac{1+2x{\text{e}}^{−2x}}{{\left(1−x{\text{e}}^{−x}\right)}^{2}}\right) & ,x\neq 0 \\ \text{α} & ,x=0\end{matrix}\right.\)

If f is continuous at x = 0, then α is equal to

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