Are there infinite combinations of Euler angles to describe the same rotation?

Question

In XYZ convention, the Euler angles (0, 180, 0) describe the same rotation as (180, 0, -180).

• Are there always multiple ways to describe the same rotation with Euler angles?
• Is there even an infinite number of ways?
• If so, how can this be proved?

EDIT: Of course, I do not mean the 360° periodicity of angles!