[math-fun] Does this define sin(z)?

1) sin(0) := 0 and 2) |sin(x) - sin(y)| ≤ |x - y| and 3) sin(x) = sin(x/3) (3 - 4 sin(x/3)^2). Note that 2) isn't even true, e.g. x=0, y=i. If this means "No", then what about for real z? —rwg