JEE Maths#4

Algebra Level 4

Let $z_1$, $z_2$ and $z_3$ be three points on $|z|=1$ in the complex plane and $z_1 + z_2 + z_3 = 0$. If $\theta_1$, $\theta_2$ and $\theta_3$ are the arguments of $z_1$, $z_2$ and $z_3$ respectively, find the value of

$\cos(\theta_1-\theta_2) + \cos(\theta_2-\theta_3) + \cos (\theta_3 -\theta_1)$



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