Concept:
Use the geometric progression condition \(b^2 = ac\) to form an equation, solve for \(\cos\theta\) using algebraic manipulation, and then find all solutions in the given interval.
Step 1: Apply the G.P. condition.
Given \(\frac{1}{2}\sin\theta, \cos\theta, \cot\theta\) are in G.P.:
\[
\cos^2\theta = \left(\frac{1}{2}\sin\theta\right)(\cot\theta) = \frac{1}{2}\sin\theta \cdot \frac{\cos\theta}{\sin\theta} = \frac{1}{2}\cos\theta.
\]
Rearrange:
\[
\cos^2\theta - \frac{1}{2}\cos\theta = 0 \implies \cos\theta\left(\cos\theta - \frac{1}{2}\right) = 0.
\]
Step 2: Solve for \(\theta\) in \((-2\pi, 2\pi)\).
Case 1: \(\cos\theta = 0 \implies \theta = \frac{\pi}{2} + n\pi\).
In \((-2\pi, 2\pi)\): \(\theta = -\frac{3\pi}{2}, -\frac{\pi}{2}, \frac{\pi}{2}, \frac{3\pi}{2}\) (4 solutions).
Case 2: \(\cos\theta = \frac{1}{2} \implies \theta = 2n\pi \pm \frac{\pi}{3}\).
In \((-2\pi, 2\pi)\): \(\theta = -\frac{5\pi}{3}, -\frac{\pi}{3}, \frac{\pi}{3}, \frac{5\pi}{3}\) (4 solutions).
Step 3: Count total solutions and write the final answer.
Total solutions = 4 + 4 = 8.
\[
\boxed{8}
\]