# If tanx + tan 2x + root3 tanx tan 2x = root 3, Then​a. x=(6n+1).pi/18 all n belongs to I​b. x=(6n+1).pi/9 all n belongs to I​c. x=(3n+1).pi/9 all n belongs to II want answer with full solution.

$\tan x+\tan2x=\sqrt3(1-\tan x+\tan2x) \\ \implies\tan(x+2x)=\sqrt3=\tan\dfrac\pi3 \\3x=n\pi+\dfrac\pi3 \text{ where } n \text{ is any integer}$