substitute z = tan x
rewrite
[tex]3z^3 = z\\3z^3-z = 0\\z(3z^2-1)=0[/tex]
this has three solutions:
(1) z = 0
(2+3)
[tex]3z^2 = 1\\|z| = \frac{1}{\sqrt{3}}\\[/tex]
[tex]z = \pm \frac {1}{ \sqrt{3}}[/tex]
So, in the range [tex]0\leq x\leq 360[/tex] these all are solutions:
for (1) tan x is 0 for x=0, 180, and 360 degrees
for (2) tan x is 1/sqrt(3) for π/6 and 7π/6
for (3) tan x is -1/sqrt(3) for -π/6 and 5π/6
