Thomas' Calculus 13th Edition

$-(\dfrac{\pi}{4})$
Consider $l=\lim\limits_{(x,y,z) \to (1,-1,-1)} \tan^{-1} (x+y+z)$ and $l=\tan^{-1} (1-1-1)=\tan^{-1} (-1)$ Hence, $l=-\tan^{-1} (\tan (\dfrac{\pi}{4}))=-(\dfrac{\pi}{4})$