If \( x_{i}0 \) for \( 1 \leq i \leq n \) and \( x_{1}+x_{2}+\ldots+x_{n}=\pi \) then the greate...

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If \( x_{i}0 \) for \( 1 \leq i \leq n \) and \( x_{1}+x_{2}+\ldots+x_{n}=\pi \) then the greatest value of the sum \( \sin x_{1}+\sin x_{2}+\ldots+\sin x_{n} \) is equal to
(a) \( n \)
(b) 0
(c) \( n \sin \left(\frac{\pi}{n}\right) \)
(d) \( \frac{n}{2} \)
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