# Understanding the constant 6.697374558 when finding GMST

I'm trying to understand the constant 6.697374558 mentioned in this question:

The Astronomical Almanac gives an expression for approximate mean sidereal time, in hours:

$$\mathit{GMST}=6.697374558+0.06570982441908D_{0}+1.00273790935H+0.000026T^{2}$$

I've googled 6.697374558 and found it described here as:

“6.697374558 was the Greenwich hour angle of the Sun at Epoch 2000”.

However, when I input the Sun's RA (18h 45.1m) at 12pm 1 January 2000 into an online RA to hour angle calculator (for the Greenwich meridian) I get 23h 56m 44.55s. Any idea what I'm doing wrong? I'm new to all this, so apologies if I've made any basic errors.

At epoch J2000.0, D0=-0.5, H=12, and T=0, so \begin{align} GMST &= 6.6974 - 0.0329 + 12.0329 \\ &= 6.6974 + 12 \\ &= 18.6974 \end{align} or 18:42:51, about 2 minutes less than the RA of the Sun on that date. The difference between UTC and TT in 2000 accounts for the 1 minute remainder.