I'm following the instructions given here for calculating the apparent position of the planets in the sky and I've come to calculating the sidereal time in section 1.8.
The formula for calculating the sidereal time at Greenwich at a given moment is given as: $$\Theta = M_E + \Omega_E + \omega_E + 15^\circ t $$ Where (all angles are in degrees) $M_E$ is the mean anomaly of the earth at that instant, $\Omega_E$ is the longitude of the ascending node for the Earth, $\omega_E$ is the argument of the periapsis for the Earth, and $t$ is the number of hours since the most recent midnight at Greenwich.
Where does this formula come from? I cannot find any other sources that use orbital elements to calculate sidereal times. Instead, they all appear to use 1st or 2nd order polynomials in $t$ with hardcoded coefficients to (approximately) calculate the sidereal time.