Maximize complex numbers

Algebra Level 4

Determine the largest real number $\color{#3D99F6}{k}$ such that $\large | z_1z_2 + z_2z_3 + z_3z_1 | \geq \color{#3D99F6}{k} | z_1 + z_2 + z_3|$ for all complex numbers $z_1 , z_2 , z_3$ with unit absolute value.

3 6 None of these 2 7 4 5 1