Well I was hoping to find some indications of those mysterious angles you have and see what are the right english expression/translation for them
Unfortunately, I cannot find those angles, even within the best Plastic theory books such as
The mathematical Theory of Plasticity
Oxford, 1950, 355 pp.
and I got other paper but nothing in it either, so basically I cannot answer to your question as I cannot recognized those angles, which somehow measure the angle between the second (or it s cubed) and the third invarient tensor
I need much more to understand the relations and specially I would need figures or drawings to see the geometrical relationship between those invarients