On Wednesday, November 1, 2017 at 12:40:35 PM UTC, Gerald Kelleher wrote:
When the rotation responsible for the Polar day/night cycle is combined with daily rotation at our latitudes, the combination of these rotations create both the natural noon variations and the seasons.

This is wrong: the equation of time is not one sinusoid added to correct the time, it is two - one for the angle of the Earth's tilt (which is the one you say is responsible for polar day-night) and another one for the earth's elliptical orbit.