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If \( 2(\cos (\alpha-\beta)+\cos (\beta-\gamma)+\cos (\gamma-\alpha)+3=0 \), prove
\( \mathrm{P} \) that \( \frac{d \alpha}{\sin (\beta+\theta) \sin (\gamma+\theta)}+\frac{d \beta}{\sin (\alpha+\theta) \sin (\gamma+\theta)}+ \)

W
\[
\frac{d \gamma}{\sin (\alpha+\theta) \sin (\beta+\theta)}=0,
\]
where, ' \( \theta \) ' is any real angle such that \( \alpha+\theta, \beta+\theta, \gamma+\theta \) are not the multiple of \( \pi \).
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