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If \( z=\cos \theta+i \sin \theta \) is a root of
\[
x^{n}+p_{1} x^{n-1}+p_{2} x^{n-2}+\ldots+p_{n}=0,
\]
where \( p_{1}, p_{2}, \ldots, p_{n} \in \mathbf{R} \),
then the value of
\( 7\left(p_{1} \sin \theta+p_{2} \sin 2 \theta+\ldots+p_{n} \sin (n \theta)\right) \) is
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