Ah, the first method is to get y=sin(-x) by making y=sinx symmetrical about X, and then translate π/3 units to the left to get y=-sin(x+π/3).

The second one is y = sin (x+4 π/3) = sin [(x+π/3)+π] =-sin (x+π/3).

Similarly, the third type is y = sin (x-2π/3) = sin [(x+π/3)-π] =-sin (x+π/3).