10. If $z_{1}, z_{2}, z_{3}$ satisfy $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=1, z_{1}+z_{2}+z_{3}=1, z_{1} z_{2} z_{3}=1$, then $\left(z_{1}, z_{2}, z_{3}\right)$ $=$ . $\qquad$
10. $(1, \mathrm{i},-\mathrm{i})$ and its 5 other permutations $\quad \overline{z_{1} z_{2}}+\overline{z_{2} z_{3}}+\overline{z_{1} z_{3}}=1, z_{1} z_{2}+z_{2} z_{3}+z_{1} z_{3}=1$ so $z_{1}, z_{2}, z_{3}$ are the three roots of $x^{3}-x^{2}+x-1=0$