Let \( z=\frac{1+2(\sin \theta) i}{1-(\sin \theta) i} \) \( \mathrm...

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Let \( z=\frac{1+2(\sin \theta) i}{1-(\sin \theta) i} \)
\( \mathrm{P} \) Find the sum of all values of \( \theta \in[0,4 \pi] \) such that \( z \) is purely real.

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