Are you trying to say it has multiple solutions because the domain of arctan is from -∞ to ∞think about a graph of the function
y = tanx
it basically repeats along the axis every 2.pi
when you take the arctan, you can think of it as picking a y value, tracing it out to across to where it intersects the curve, and dropping down to the x value, giving you
x = arctan(y)
how do you choose a curve to use....? multiple solutions... how many are there?