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Let \( z=\cos \theta+i \sin \theta \). Then, the value of \( \sum_{m=1}^{15} \operatorname{Im}\left(z^{2 m-1}\right) \) at
\( \mathrm{P} \) \( \theta=2^{\circ} \) is

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(a) \( \frac{1}{\sin 2^{\circ}} \)
(b) \( \frac{1}{3 \sin 2^{\circ}} \)
(c) \( \frac{1}{2 \sin 2^{\circ}} \)
(d) \( \frac{1}{4 \sin 2^{\circ}} \)
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