Let \( A = \left\{ \ \theta \in (0, 2\pi) : \dfrac{1 + 2i \sin \theta}{1 - i \sin \theta} \ \text{is purely imaginary} \ \right\}. \) Then the sum of the elements in \( A \) is:
\( 3\pi \)
\( 2\pi \)
\( 4\pi \)
\( \pi \)
