Find all solutions of the equation. Express the solutions in radians in the form α+nπ, where α is in ​[0,2π​). tan(x) = -1. The examples has us use the form a=T^-1 (k) to solve T(x)=k, where T(x) is a trig function.

The book says the solution is x=3π/4 + nπ. But if arctan has a range of (-π/2,π/2) then how can α be equal to 3π/4? And 3π/4 isn't equal to tan^-1 (-1) soo?? I think the solution is x=-π/4+nπ.