[tex]\begin{gathered} \sqrt[]{3}\tan ^2x+\tan x=0 \\ \sqrt[]{3}\tan ^2x=-\tan x \\ \text{Dividing both sides by tan x} \\ \sqrt[]{3}\tan ^{}x=-1 \\ \tan x=\frac{1}{\sqrt[]{3}} \\ x=\tan ^{-1}\frac{1}{\sqrt[]{3}} \\ x=-30\text{ deg = -30 + 360 = 330} \\ 330\text{ degr = }\frac{330\pi}{360}=\frac{11\pi}{12} \\ x=-30\text{ deg = -30 + 180 = 150} \\ 150\text{ degr = }\frac{150\pi}{360}=\frac{5\pi}{12} \\ x\text{ = 0 is the trivial solution.} \\ \text{Therefore, x = }\frac{11\pi}{12},\text{ x =}\frac{5\pi}{12},x=0 \end{gathered}[/tex]
OPTION C
