Let \(M\) and \(m\) respectively be the maximum and minimum values of the function \(f(x)=\tan ^{-1}(\sin x+\cos x)\) in…

Let \(M\) and \(m\) respectively be the maximum and minimum values of the function \(f(x)=\tan ^{-1}(\sin x+\cos x)\) in \(\left[0, \frac{\pi}{2}\right]\). Then the value of \(\tan (M-m)\) is equal to

[JEE Main 2021, 27 Aug (Shift 2)]