so arctan is just the inverse of tangent. we use it to solve for an angle. so in general:

if sinx = y then x = arcsiny

if cosx = y then x = arccosy

if tanx = y then x = arctany

and so on

then you usually have to add k*pi, or 2k*pi depending on what interval you want to solve for and the particular problem. these functions are periodic, so they repeat the same values over and over, that's what the multiples of pi take care of

do you understand how they ended up with tan@ = -2/3?