The God of all Problems -2

$\large |z_1 + z_2 | \geq \frac12 \left( |z_1 | + |z_2 | \right) \left | \frac{z_1}{|z_1|} + \frac{z_2}{|z_2|} \right |$

If $z_1$ and $z_2$ are two arbitrary complex numbers, is the inequality above true?