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To solve the inequality \( \tan(x) < \sqrt{3} \), we can start by identifying the angle whose tangent is \( \sqrt{3} \).

In trigonometry, we know that:

\[ \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \]

The tangent function is periodic with a period of \( \pi \). Thus, the general solutions for \( \tan(x) = \sqrt{3} \) occur at:

\[ x = \frac{\pi}{3} + n\pi \quad \text{for } n \in \mathbb{Z} \]

Now, we need to find the intervals where \( \tan(x) < \sqrt{3} \). The tangent function increases in each period, so within one period from \( 0 \) to \( \pi \):

• \( \tan(x) < \sqrt{3} \) for \( 0 < x < \frac{\pi}{3} \)
• Beyond \( \frac{\pi}{3} \) but before \( \pi \), \( \tan(x) \) exceeds \( \sqrt{3} \).

The pattern repeats every \( \pi \), which means we can express the solution as:

\[ x \in (n\pi, n\pi + \frac{\pi}{3}) \quad \text{for } n \in \mathbb{Z} \]

So, the complete solution to the inequality \( \tan(x) < \sqrt{3} \) is:

\[ x \in \bigcup_{n \in \mathbb{Z}} \left( n\pi, n\pi + \frac{\pi}{3} \right) \]

This gives us all the intervals where the tangent of \( x \) is less than \( \sqrt{3} \).