Complex Number Equation Sum (Jee Mains)

Algebra and Representation of Complex Numbers

Medium

Complex Number Equation Sum

Let A = $\left\{ {\theta \in [0,\;2\pi ]:1 + 10\operatorname{Re} \left( {\frac{{2\cos \theta + i\sin \theta }}{{\cos \theta - 3i\sin \theta }}} \right) = 0} \right\}$ ,
Then $\sum\limits_{\theta \in A} {{\theta ^2}}$ is equal to

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