Is this an equivalence relation (reflexivity, symmetry, transitivity) 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.

Your relation is
$$sRq\iff \theta(s)\not \equiv 0\text{ and }\theta(q)\not \equiv 0 \mod 2\pi$$
for $s,q\in \mathbb{C}$.
For symmetry:
$$sRq\iff \theta(s)\not \equiv 0\text{ and }\theta(q)\not \equiv 0 \mod 2\pi \iff qRs$$
For transitivity:
$$sRq\text{ and }qRp\iff \theta(s)\not \equiv 0\text{ and }\theta(q)\not \equiv 0\text{ and }\theta(p)\not \equiv 0 \mod 2\pi\implies sRp$$
Reflexitivity is:
$$sRs\iff \theta(s)\not \equiv 0\mod 2\pi$$
That clearly depends on your choice of $\theta$. Therefore, $R$ is an equivalence relation iff $$\theta(\mathbb{C})\cap \left\{2k\pi:k\in \mathbb{Z}\right\}=\emptyset$$
