As y=arctanx is the inverse of y=tanx it can't be done. As we know tan goes on forever but when working in degrees you can never input values of 90, 270 and so on. This makes it impossible to define a domain for y=tanx as you'd have an infinite number of x != 90 and so on exceptions.
Additonaly the range of tan goes on into infinity which makes it even more tricky. The range however can technically be defined as all real values of y: y in RR although its not good practice.
For these reasons it is not possible to define arctan's domain or range in a mathematically correct way however you can technically define its domain as all real values of x: x in RR since the range of tan is that. Howerver it is impossible to define the range of y=arctanx since you'd have to have an infinite number of exceptions.