Evaluate `sin(pi/n)+sin((3pi)/n)+sin((5pi)/n)+........` to n terms.

Explanation

To evaluate the series \( S = \sin\left(\frac{\pi}{n}\right) + \sin\left(\frac{3\pi}{n}\right) + \sin\left(\frac{5\pi}{n}\right) + \ldots \) up to \( n \) terms, we can recognize that this is an arithmetic progression (AP) in terms of the angles. The common difference between the angles is \( \frac{2\pi}{n} \).

### Step-by-Step Solution:

1. **Identify the first term and common difference:**
- The first term \( a = \frac{\pi}{n} \)
- The common difference \( d = \frac{2\pi}{n} \)

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