I have been studying pointwise and uniform convergence of sequences of functions and i am stuck with this question,

Show that lim(Arctan nx) = (pi/2)sgnx for x in R.

I believe that we will have to take three cases for the limit function f(x), namely when it is equal to -(pi/2), 0 and (pi/2).

But i cannot figure out , a way to show that |fn(x) -f(x)|< epsilon.

Please HELP.