हल कीजिए - `-tan theta + tan (theta +pi/3) + tan (theta+(2pi)/3)=3`

Explanation

दिया है -
`tan theta + tan(theta+pi/3)+ tan (theta+(2pi)/3)=3`
`rArr tan theta+ (tan theta+tan. pi/3)/(1-tan theta tan. pi/3)+(tan theta +tan. (2pi)/3)/(1-tan theta tan. (2pi)/3) = 3`
`rArr tan theta + (tan theta +sqrt3)/(1-sqrt3*tan theta) +(tan theta-sqrt3)/(1+sqrt3* tan theta) = 3`
`rArr tan theta + (8 tan theta)/(1-3 tan^(2) theta) = 3`
`rArr (tan theta -3 tan^(3) theta + 8 tan theta)/(1-3 tan ^(2) theta) = 3`
`rArr (3(3tan theta - tan^(3) theta))/(1-3tan^(2) theta) = 3`
`rArr 3 tan 3 theta= 3`
अर्थात `tan 3 theta = 1`
`rArr tan 3 theta = tan. pi/4`
`rArr 3 theta = n pi + pi/4 , n in Z`
` :. theta = (n pi)/3 + pi/12, n in Z`