What is the angle x if tan 3x -tan^3 x=0?

To find the angle x if tan 3x -2tan^3
x=0.

tan3x = (3tanx-tan^3x) / (1-3tan^2x) is an
identity.

So we use this in the given
equation:

(3tanx-tan^3x) / (1-3tan^2x) - 2tan^3x =
0.

(3tanx-tan^3x) -  (1-3tan^2x)*2tan^3x =
0.

tanx {3 -tan^2x - 2tan^2 + 6tan^4x} =
0

tanx (3-3tan^2+6tan^4x) = 0. We divide by
3.

tanx (tan^4x-3tan^2x +1) =
0.

tanx(tan^2x-1)(1+2tan^2) =
0.

tanx = 0, tan^2-1 = 0, or 1+2tan^2x =
0.

tanx = 0, ortan^2 =1, or tan^2 = 1. So tanx = +or-
1.

So x = npi, or x= npi+pi/4, or npi - pi/4, for n =
0,1,2,..