# Its complex with geometry

Algebra Level 5

If $$\displaystyle \large{\text{ arg }(\frac{z-1}{e^{i\theta}}+\frac{e^{i\theta}}{z-1})=0 \text{ or }\pi}$$

where $$\theta \in \mathbb{ R}$$ and $$z$$ is a variable complex number. If the locus of $$z$$ is a curve $$C$$ then find the area of equilateral triangle inscribed in it.

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