I mean the angles between arbitary 2-plane and euclidean orthonormal 2-planes which common origin lies at that 2-plane ⊂ R⁴. I think the orthonormality of 2-planes (bivectors) is unambiguous in normal cartesian 4d system, isn't it?
I got a solution that three could be enough; angles by ruled parity in relation to e.g. xy, yz, zw -planes (set 4d as x, y, z, w coordinates). The unknown 2-plane goes through the origin, you remember.
I tried to check all the degrees of freedom. Can anyone study a solution?
Let yz be the 2-plane under operations.
Now, we can define isoclinic rotations α (xy, zw), β (yz, wx) and γ (xz, yw).
My statement: In order α -> β -> γ with appropriate parameters we can rotate yz-plane to any 2-plane through the origin of euclidean R⁴.
How to proof?