1. The problem is to find the value of $\cot(-300^\circ)$. 2. Recall that the cotangent function is the reciprocal of the tangent function: $$\cot \theta = \frac{1}{\tan \theta}$$ 3. Also, cotangent is periodic with period $180^\circ$, so: $$\cot(-300^\circ) = \cot(-300^\circ + 360^\circ) = \cot(60^\circ)$$ 4. We know from the unit circle that: $$\tan 60^\circ = \sqrt{3}$$ 5. Therefore: $$\cot 60^\circ = \frac{1}{\tan 60^\circ} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$ 6. So the final answer is: $$\cot(-300^\circ) = \frac{\sqrt{3}}{3}$$