You can use any Floodfill method to get all integer points in the sector. Precalculate starting and ending angles as
S_Angle = Center_Bearing - Pi/6
E_Angle = Center_Bearing + Pi/6
Important values:
S_Cos = Cos(S_Angle)
S_Sin = Sin(S_Angle)
E_Cos = Cos(E_Angle)
E_Sin = Sin(E_Angle)
Border conditions for sector floodfill:
(x-x0)*S_Sin-(y-y0)*S_Cos >= 0 //point is left to starting ray
(x-x0)*E_Sin-(y-y0)*E_Cos <= 0 //point is right to ending ray
(x-x0)^2+(y-y0)^2 <= R^2 //point is in the range
(probably you may need to exchange >= and <= in the first inequalities pair)