De Moivre's theorem

Let $S=\left\{z\in\mathbb C:z^2+\sqrt6\,iz-3=0\right\}$. Then $\displaystyle\sum_{z\in S}z^8$ is equal to :

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