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If $x>0, y>0, z>0, x y+y z+z x < 1$ and if $\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi$, then $x+y+z$ equals to
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$x y z$
$\begin{aligned} & \text { Given, } \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi \\ & \Rightarrow \quad \tan ^{-1}\left(\frac{x+y+z-x y z}{1-x y-y z-z x}\right)=\pi \\ & \Rightarrow \quad \frac{x+y+z-x y z}{1-x y-y z-z x}=\tan \pi=0 \\ & \Rightarrow \quad x+y+z=x y z\end{aligned}$
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