It seems that one can color a 15-15-15-30 trapezoid with the given tiles. Here is a picture (sorry about adjacent figures that are the same color, I used random colors so hopefully there are no ambiguities):

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/vAh1v.png

In particular, OP pointed out that these scaled 1-1-1-2 trapezoids can tile any equilateral triangle whose side length is a multiple of three. So the original tile can tile any equilateral triangle whose side length is a multiple of 15.

I bet we didn't see answers for smaller $n$ due to an Aztec-diamond-like boundary condition with the corners.