This may be a start:
Plot[Evaluate@Table[Re[ArcTan[x, y]], {y, -3, 3}], {x, -3, 3},
PlotRange -> {-3, 3}, Frame -> True,
BaseStyle -> {FontFamily -> "Helvetica", FontSlant -> Italic,
FontSize -> 20},
PlotStyle -> Table[ColorData["Rainbow"][c], {c, Subdivide[6]}]]
