$S$ converges for all $\theta \in (0, 2\pi)$.

$S$ converges absolutely for all $\theta \in (0, 2\pi)$.

The partial sums of $\sum_{n=2}^N \cos(n \theta)$ are bounded for any $\theta \in (0, 2\pi)$.

$S$ converges conditionally for all $\theta \in (0, 2\pi)$.