The given expression simplifies to:

$4\pi |n|$

Would you like a detailed step-by-step explanation of the simplification process?

Here are 5 related questions for further exploration:

1. How does the absolute value function impact the final result?
2. What is the role of trigonometric identities in simplification?
3. How would the result change for different values of $n$?
4. Can the simplification process be extended to complex numbers for $n$?
5. How does the presence of $\pi$ in the expression affect periodicity?

Tip: Simplifying trigonometric expressions often involves using known values of sine and cosine at multiples of $\pi$.