Definite integral from Riemann Sum

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I'm trying to convert this Riemann Sum into the definite integral, but I'm stuck. $$\lim_{n \rightarrow \infty } \sum_{k=n}^{2n} \sin\left(\frac{\pi}{k} \right)$$

I know the theory and I solved other exercises. The problem with this one is finding the right guess.

I tried pulling out $n$ from the sum.

Another attempt was to subtitute $$k=\frac{1}{i}$$