Equivalence Relation/Examples/Equal Sine of pi x over 6 on Integers

Example of Equivalence Relation
Let $\Z$ denote the set of integers.

Let $\RR$ denote the relation on $\Z$ defined as:
 * $\forall x, y \in \Z: x \mathrel \RR y \iff \sin \dfrac {\pi x} 6 = \sin \dfrac {\pi y} 6$

Then $\RR$ is an equivalence relation.