Find the general solution of equation $$tanx=\frac{1}{\sqrt3}$$.

Correct option is C

​$$\begin{aligned}&\text{First, find the principal solution (i.e., the smallest positive angle } x \text{ that satisfies the equation).} \\&\text{We know that:} \\&\tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} \\&\text{Thus, one solution is:} \\&x = \frac{\pi}{6} \\\\&\textbf{Determine the General Solution} \\&\text{The tangent function has a period of } \pi, \text{ meaning:} \\&\tan x = \tan(x + n\pi) \quad \text{for any integer } n. \\&\text{Therefore, the general solution is:} \\&x = \frac{\pi}{6} + n\pi \quad \text{where } n \in \mathbb{Z} \text{ (i.e., } n = 0, \pm1, \pm2, \ldots \text{)}\end{aligned}$$​​