8.4. For all triples $(x, y, z)$ satisfying the system

$$
\left\{\begin{array}{l}
\sqrt{3} \cos x=\operatorname{ctg} y \\
2 \cos y=\operatorname{tg} z \\
\cos z=2 \operatorname{ctg} x
\end{array}\right.
$$

find the smallest value of the expression $\sin x+\sin z$.
Answer. $-\frac{7 \sqrt{2}}{6} \approx-1.65$.