The segment and a grid check

You will write functions for the area of a segment. Then you will check the formula in a different way, by counting small squares on a grid.

The idea. The minor segment is the sector minus the triangle $OAB$. A segment can also be counted: lay a fine grid over the circle and count the grid squares whose centres lie in the segment. The count should agree with the formula.

Your tasks.

1. In minor_segment, return the area of the minor segment for a radius and an angle in degrees, rounded to $4$ decimals.
2. In major_segment, return the area of the major segment, rounded to $4$ decimals.
3. In segment_by_grid, return the count of grid squares in the segment times the area of one square, for the grid in the starter.
4. Set smallest_angle to the smallest whole-degree angle for which the minor segment of a circle of radius $10$ has an area of at least $10$.