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The value of
\[
\sin ^{2} \alpha+\sin ^{2}(\alpha+\beta)+\sin ^{2}(\alpha+2 \beta)+\ldots+\sin ^{2}(\alpha+(n-1) \beta)
\]
is equal to
(a) \( \frac{1}{2}\left[n+\frac{\sin n \beta}{\sin \beta} \cos \{2 \alpha+(n-1) \beta\}\right] \)
(b) \( \frac{1}{2}\left[n-\frac{\sin n \beta}{\sin \beta} \cos \{2 \alpha+(n-1) \beta\}\right] \)
(c) \( \left[n+\frac{\sin n \beta}{\sin \beta} \cos \{2 \alpha+(n-1) \beta\}\right] \)
(d) \( \left[n-\frac{\sin n \beta}{\sin \beta} \cos \{2 \alpha+(n-1) \beta\}\right] \)
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