1. **Problem statement:** Given $\tan \theta = 2$, find $\tan(3\theta)$.\n\n2. **Formula used:** The triple-angle formula for tangent is:\n$$\tan(3\theta) = \frac{3\tan\theta - \tan^3\theta}{1 - 3\tan^2\theta}$$\nThis formula helps us express $\tan(3\theta)$ in terms of $\tan\theta$.\n\n3. **Substitute the given value:** Since $\tan \theta = 2$, substitute into the formula:\n$$\tan(3\theta) = \frac{3(2) - 2^3}{1 - 3(2^2)} = \frac{6 - 8}{1 - 3(4)}$$\n\n4. **Simplify numerator and denominator:**\nNumerator: $6 - 8 = -2$\nDenominator: $1 - 12 = -11$\n\n5. **Calculate the final value:**\n$$\tan(3\theta) = \frac{-2}{-11} = \frac{2}{11}$$\n\n**Answer:** $\boxed{\tan(3\theta) = \frac{2}{11}}$