Find the complex numbers $\displaystyle z_1, z_2, z_3$, so that $\displaystyle |z_1|=|z_2|=|z_3|=1$ and $\displaystyle z_1+z_2+z_3=z_1\cdot z_2\cdot z_3=1$.

Comment>

I know that $\displaystyle z_1, z_2, z_3 $ are on circle with r=1.

And know $\displaystyle x_1+x_2+x_3=1$.

How to combine it for product?

Thank you.