At what point does the ecliptic cut the celestial equator?
Celestial equator is Earth's equator zoomed, in its plane, as the equator (great circle ) of the celestial sphere. The line of intersection of this plane and ecliptic contains a diameter of Earth...
Celestial sphere is virtual. Its radius is undefined.
Ecliptic is Earth's orbital plane, cutting the Earth's surface along a great circle.
Celestial equator is the zooming of our equator,in its plane, onto the virtual celestial sphere.
It is meaningful to identify the plane of celestial equator as the plane of Earth's equator.
Of course, the rotating and tilted Earth's equator transits the ecliptic, at the eds of a diameter,