How can I find lattice points of a circle sector?

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I have a 10x10 grid, and I'd like to find how many lattice points are inside a sector of a circle of any angle.

Circle details

  • Radius: 5
  • Center: (0, 0)
  • Sector 1: 65 degrees
  • Sector 2: 300 degrees

How do I find how many integer points are inside each of those sectors?