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

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)]