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Below is a pseudocode of solution that works for me:

  • Get rotation of tool tip in the bin's frame (r1)
  • get target's rotation in bin's frame (r2)
  • calculate r12
  • Form a new rotation r3 from r12 with the rz = 0
  • required rotation = r13

There may be issues with pre and post multiplications in the notations, but I hope the idea is clear.