Cosmic Penguin

Let the first point of Aries, where right ascension RA = 0, be A, G be the geocenter, S the sun and s the sat. Then when the sat is passing the node, LAN is the A-G-s angle and GMT-GST is the A-G-S angle. So, LAN+GMT-GST is the s-G-S angle which is the SSO local time

Hence you need to find the time at which the sat passes through the node, then calculate GMT time of day and the sidereal time GST at that moment