1. **State the problem:** Find the fundamental period of the function $$f(x) = \tan\left(\frac{2x - 1}{3}\right)$$. 2. **Recall the period of tangent function:** The basic tangent function $$\tan(x)$$ has a fundamental period of $$\pi$$. 3. **Period formula for transformed tangent:** For $$f(x) = \tan(bx + c)$$, the period is $$\frac{\pi}{|b|}$$. 4. **Rewrite the argument:** The argument of the tangent is $$\frac{2x - 1}{3} = \frac{2}{3}x - \frac{1}{3}$$. 5. **Identify the coefficient of $$x$$:** Here, $$b = \frac{2}{3}$$. 6. **Calculate the period:** $$ \text{Period} = \frac{\pi}{|b|} = \frac{\pi}{\frac{2}{3}} = \pi \times \frac{3}{2} = \frac{3\pi}{2} $$ 7. **Final answer:** The fundamental period of $$f(x)$$ is $$\boxed{\frac{3\pi}{2}}$$.