If tan $\theta$ + tan 2$\theta$ + tan 3$\theta$ = tan $\theta$.tan 2$\theta$. tan 3$\theta$, then the general value of the $\theta$ is ______.

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If tan $\theta$ + tan 2$\theta$ + tan 3$\theta$ = tan $\theta$.tan 2$\theta$. tan 3$\theta$, then the general value of the $\theta$ is ("n"pi)/6. Explanation: tan (A + B + C) = `(tan A + tan B - tanA. tan B. tan C)/(1 - tan A.tan B - tan B.tanC - tan C.tan A)` Since, tan $\theta$ + tan 2$\theta$ + tan 3$\theta$ = tan $\theta$.tan 2$\theta$.tan 3$\theta$, we get, tan ($\theta$ + 2$\theta$ + 3$\theta$) = $\theta$ $\therefore$ tan 6$\theta$ = 0 $\therefore$ 6$\theta$ = n$\pi$ $\theta$ = (npi)/6

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