Rotation around non orthogonal axis

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I am trying to wrap my head around some problem. How to calculate correct angle of rotation, when one of the rotation axis isnt orthogonal to machining plane.

Lets imagine that we put a box on the table c axis, and want to machine its right/left side.

On orthogonal kinematics, i would simply rotate B axis to B-90 or B90

Orthogonal kinematics

So rotation of the object, equals rotations of machine axes.

In the image below, B axis is rotating at plane shifted by 45 degree. So when i want to machine left/right side of the box, i would have to rotate both B and C axis ( by C90/C270 and B180)

Nutated B axis in table

How to find this real B and C angle? (how to take into account that B axis of rotation is angled at 45 degree and find those 2 angles).