1. **State the problem:** Solve the equation $3\tan x = \sqrt{3}$ for $x$. 2. **Isolate $\tan x$:** Divide both sides by 3: $$\tan x = \frac{\sqrt{3}}{3}.$$ 3. **Recall the values of $\tan x$:** The tangent of $\pi/6$ (30 degrees) is $\tan \frac{\pi}{6} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$. 4. **General solution for $\tan x = \tan \theta$:** Since tangent has a period of $\pi$, the general solution is: $$x = \frac{\pi}{6} + \pi k, \quad k \in \mathbb{Z}.$$ 5. **Final answer:** $$x = \frac{\pi}{6} + \pi k, \quad k \in \mathbb{Z}.$$