1. The problem asks to find the value of $\cot(30^\circ)$ given that $\tan(30^\circ) = \frac{\sqrt{3}}{3}$.\n\n2. Recall the identity relating cotangent and tangent: $$\cot(\theta) = \frac{1}{\tan(\theta)}.$$\n\n3. Using this formula, substitute $\theta = 30^\circ$: $$\cot(30^\circ) = \frac{1}{\tan(30^\circ)}.$$\n\n4. Substitute the given value of $\tan(30^\circ)$: $$\cot(30^\circ) = \frac{1}{\frac{\sqrt{3}}{3}}.$$\n\n5. Simplify the fraction by multiplying numerator and denominator: $$\cot(30^\circ) = \frac{1 \times 3}{\sqrt{3}} = \frac{3}{\sqrt{3}}.$$\n\n6. Simplify $\frac{3}{\sqrt{3}}$ by dividing numerator and denominator by $\sqrt{3}$: $$\cot(30^\circ) = \sqrt{3}.$$\n\n7. Therefore, the value of $\cot(30^\circ)$ is $\sqrt{3}$.\n\nAnswer: A) $\sqrt{3}$