SOLUTION
The given equation is:
[tex]2\tan x+2\sqrt[]{3}=0[/tex]
rewrite the equation as follows:
[tex]2\tan x=-2\sqrt[]{3}[/tex]
Divide both sides by 2
[tex]\begin{gathered} \tan x=\frac{-2\sqrt[]{3}}{2} \\ \tan x=-\sqrt[]{3} \end{gathered}[/tex]
Hence the value of x is
[tex]\begin{gathered} x=\tan ^{-1}(-\sqrt[]{3})^{}_{} \\ x=\frac{2\pi}{3}+\pi n \end{gathered}[/tex]
Therefore using the given interval, the value of x is
[tex]x=120^{\circ}[/tex]
