The expression you provided is:

$\frac{111}{\tan\left(\frac{\pi}{5}\right)}$

Steps:

1. First, calculate $\frac{\pi}{5}$: $\frac{\pi}{5} \approx 0.62831853 \, \text{radians}$

2. Next, find the value of $\tan\left(\frac{\pi}{5}\right)$. Using a calculator: $\tan\left(0.62831853\right) \approx 0.726542528$

3. Finally, compute $\frac{111}{\tan\left(\frac{\pi}{5}\right)}$: $\frac{111}{0.726542528} \approx 152.762$

Result:

$\frac{111}{\tan\left(\frac{\pi}{5}\right)} \approx 152.762$

Would you like more details or have any other questions?

Related Questions:

1. What is the tangent function and how is it derived?
2. How do you convert angles between radians and degrees?
3. Can we compute trigonometric functions without a calculator?
4. What is the significance of $\pi/5$ in geometry?
5. How does the tangent function behave for other angles?

Tip: The tangent function relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.