This is a Heyacrazier puzzle, a variant of Heyacrazy.

Rules of Heyacrazy:

• Shade some cells of the grid.

• Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected.

• When the puzzle is solved, you must not be able to draw a line segment that passes through two borders, and does not pass through any shaded cells or grid vertices.

For an example puzzle and its solution, see this question.

Rule change for Heyacrazier:

• The forbidden lines are now those that pass through three borders, instead of two. Lines that pass through only two borders are acceptable.