This doesn't produce three equal angles. Indeed, the angles it produces are completely dependent upon the orientation of the line you pick to intersect the angl

This doesn't produce three equal angles. Indeed, the angles it produces are completely dependent upon the orientation of the line you pick to intersect the angle's rays with. But even using a line intersecting both rays of the angle at equal inclination, you still won't get three equal angles by trisecting this line segment and drawing rays from the origin through its new points. The middle angle will be wider than the equal outer two.