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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