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.

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