Triangle Tiling: The case $3α+ 2β= π$

An $N$-tiling of triangle $ABC$ by triangle $T$ (the ``tile'') is a way of writing $ABC$ as a union of $N$ copies of $T$ overlapping only at their boundaries. Let the tile $T$ have angles $(α,β,γ)$, and sides $(a,b,c)$. This paper takes up the case when $3α+ 2β= π$. Then there are (as was already kn