The problem on your screen asks for the exact value of $\cot 60^\circ$.

To solve this:

1. Recall that $\cot \theta$ is the reciprocal of $\tan \theta$, so: $\cot \theta = \frac{1}{\tan \theta}$
2. The tangent of $60^\circ$ is $\sqrt{3}$, so: $\cot 60^\circ = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$

Therefore, the exact value of $\cot 60^\circ$ is $\frac{\sqrt{3}}{3}$.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the exact value of $\cot 45^\circ$?
2. How can you express $\tan 60^\circ$ in terms of sine and cosine?
3. What is the general definition of $\cot \theta$ in terms of sine and cosine?
4. How can you derive the value of $\tan 60^\circ$ using an equilateral triangle?
5. What is the relationship between $\cot \theta$ and $\tan \theta$ in trigonometric identities?

Tip: Always remember that $\cot \theta = \frac{1}{\tan \theta}$, which can be particularly useful when you know the value of $\tan \theta$.