The Earth's Axial tilt is called the Obliquity of the Ecliptic and the is angle between the perpendicular to Orbit and the North Celestial Pole.
The Equatorial coordinate system is based on the 360 degree Celestial Equator Circle. The Ecliptic coordinate system is based on the 360 degree Ecliptic circle.
The mathematical conversion from Equatorial to Ecliptic is effectuated by the equation for the Ascendant
Lagna = atan ( Sin E / Cos E Cos w - Sin w Tan A )
L is the Lagna on the Ecliptic. E is the Lagna on the Celestial Equator, the Sayana Kala Lagna. The Sayana Kala Lagna, E, is reduced to the Ecliptic by this equation. The Lagna is the intersecting point between the Eastern Celestial Horizon, the Kshitija with the Ecliptic.
w is the Sun's maximum declination and A is the latitude of the place.
The above diagram is by courtesy of Wikipedia
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