If the domain of the function \(f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left\{\log _{ e }(3-x)\right\}^{-1}\) is \(…

If the domain of the function \(f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left\{\log _{ e }(3-x)\right\}^{-1}\) is \([-\alpha, \beta)-\{\gamma\}\), then \(\alpha+\beta+\gamma\) is equal to :

[JEE Main 2024, 30 Jan (Shift 1)]