Answer
$ \tan A\tan B \tan C=\tan A+\tan B+\tan C$
Work Step by Step
Let us consider $x-y=A; y-z=B, z-x=C$
Now, we have
$\tan C=-\dfrac{\tan A+\tan B}{1-\tan A\tan B}$
or, $\tan C(1-\tan A\tan B) =-[\dfrac{\tan A+\tan B}{1-\tan A\tan B}](1-\tan A\tan B)$
or, $\tan C(1-\tan A\tan B) =-(\tan A+\tan B)$
Thus, we have
$ \tan A\tan B \tan C=\tan A+\tan B+\tan C$
