kt.k theory homology - K_2 of rings of algebraic integers

It's a theorem of Garland that $K_2(R)$ is finite. Perhaps the best way to get a handle on it is to use Quillen's localization sequence
$$0rightarrow K_2(R)rightarrow K_2(F)stackrel{T}{rightarrow} oplus_v k(v)^*rightarrow 0,$$
where $F$ is the fraction field and the $k(v)$ are the residue fields. The map $T$ is the sum of the tame symbols, which is surjective by a theorem of Matsumoto. The injectivity on the left follows from the vanishing of $K_2$ for finite fields.

This isn't much of an answer, but considering $K_2(R)$ as a subgroup of $K_2(F)$ seems a reasonable way to start some concrete considerations. For a detailed discussion of an algorithm that proceeds essentially along these lines ('Tate's method), see the paper

Belabas, Karim; Gangl, Herbert
Generators and relations for $K_2( O_F)$.
$K$-Theory 31 (2004), no. 3, 195--231.

Added, 8 July:

I'm sure most people know this, but I forgot to mention (for newcomers) the fact that
$$K_2(F) = F^timesotimes_{mathbf Z} F^times/langle aotimes(1-a)mid anot=0,1rangle,$$
which I suppose motivates the original question, and makes it worthwhile to view $K_2(R)$ as a subgroup.