Let $\theta(s):\mathbb{C}\to \mathbb{R}$ be a well defined function. I define the following relation in $\mathbb{C}$.
$\forall s,q \in \mathbb{C}: s\mathbin{R}q\iff\theta(s)\ne 0 \pmod {2\pi}$ (and)
$\theta(q)\ne 0 \pmod {2\pi}$
The function $\pmod {2\pi}$ is the addition $\pmod {2\pi}$
My question: Is this an equivalence relation (reflexivity, symmetry, transitivity)?
The formula of $\theta(s)$ is not important for this question.