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If tantheta+tan2theta+sqrt(3)tanthetatan...

If `tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3)`, then `theta=(npi)/(3)+(pi)/(9)`.

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True
`tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3)`
`rArr" "tantheta+tan2theta=sqrt(3)-sqrt(3)tanthetatan2theta` ltBrgt `rArr" "tantheta+tan2theta=sqrt(3)(1-tanthetatan2theta)`
`rArr" "(tantheta+tan2theta)/(1-tanthetatan2theta)=sqrt(3)`
`rArr" "tan(theta+2theta)=tan""(pi)/(3)rArr tan3theta=tan""(pi)/(3)`
`therefore" "3theta=npi+(pi)/(3)`
`" "theta=(npi)/(3)+(pi)/(9)`
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