1. **State the problem:** Evaluate $\cot 300^\circ$. 2. **Recall the definition:** $\cot \theta = \frac{\cos \theta}{\sin \theta}$. 3. **Identify the quadrant:** $300^\circ$ is in the fourth quadrant where cosine is positive and sine is negative. 4. **Calculate sine and cosine:** $$\cos 300^\circ = \cos (360^\circ - 60^\circ) = \cos 60^\circ = \frac{1}{2}$$ $$\sin 300^\circ = \sin (360^\circ - 60^\circ) = -\sin 60^\circ = -\frac{\sqrt{3}}{2}$$ 5. **Compute cotangent:** $$\cot 300^\circ = \frac{\cos 300^\circ}{\sin 300^\circ} = \frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}} = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}$$ 6. **Final answer:** $\cot 300^\circ = -\frac{\sqrt{3}}{3}$. This means the correct choice is $-\frac{\sqrt{3}}{3}$.