Solve that following equations : `"tantheta"+"tan"(theta+pi/3)+"tan"(theta+(2pi)/3)=3`

Answer

`theta=(4n+1) pi/12, n in Z`

Explanation

`tan theta +tan (theta+pi//3)+tan (theta+2pi//3)=3`
or `tan theta+ (tan theta+tan (pi//3))/(1-tan theta tan (pi//3))+(tan theta + tan (2pi//3))/( 1-tan theta tan (2pi//3))`
or `tan theta + (tan theta +sqrt(3))/(1-sqrt(3) tan theta)+(tan theta -sqrt(3))/(1+sqrt(3) tan theta)=3`
or `3xx(3tan theta-tan^(3) theta)/(1-3 tan^(2) theta)=3`
or `tan 3 theta =1=tan (pi//4), n in Z`
`rArr 3 theta=n pi + pi//4, n in Z`
or `theta=(4 n+1) pi//12, AA n in Z`