### Instruction: Find $\cot (-60^\circ).$.### Response: To find the cotangent of a negative angle, I need to use the property that $\cot (-\theta) = -\cot \theta.$
This means that $\cot (-60^\circ) = -\cot (60^\circ).$
Now, I need to recall the value of $\cot (60^\circ).$
I can use the fact that $\cot \theta = \frac{1}{\tan \theta}$ and that $\tan (60^\circ) = \sqrt{3}.$
So, $\cot (60^\circ) = \frac{1}{\sqrt{3}}.$