XYZ Reference Frame

So this model has something of a back-story:

I spent two full days at work trying to solve a problem around a sequence of 3D rotations. It wasn't until I grabbed a piece of equipment that had X, Y and Z axes etched on the casing, and took it through the desired sequence of rotations that I realised what my (extremely simple) problem was. One of my rotations was inverted. It was that easy, but until I had something in my hands I could prototype the rotations with, I could not for the life of m