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

\[\cos(\theta_1-\theta_2) + \cos(\theta_2-\theta_3) + \cos (\theta_3 -\theta_1)\]