Tan x + tan 2x+ tan3x=tanx.tan 2x.tan 3x

tanx+ tan 2x= -tan 3x +tan x.tan2x.tan 3x

tanx+tan2x= -tan 3x(1-tanxtan2x) we took -tan3x common

Now cross multiplying

tanx+tan 2x UPON 1-tanx. Tan2x= - tan 3x

which is equal to tan(x+2x)= -tan 3x

tan 3x=-tan 3x

tan3x=0

3x= n pie, therefore x =n pie/3

tanx+ tan 2x= -tan 3x +tan x.tan2x.tan 3x

tanx+tan2x= -tan 3x(1-tanxtan2x) we took -tan3x common

Now cross multiplying

tanx+tan 2x UPON 1-tanx. Tan2x= - tan 3x

which is equal to tan(x+2x)= -tan 3x

tan 3x=-tan 3x

tan3x=0

3x= n pie, therefore x =n pie/3