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Jan 22nd, 2018
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  1. Solve[{RotationMatrix[x1, {y1, y2, y3}].({-1, 1, -1}/
  2. Norm[{-1, 1, -1}]) == {1, 0, 0},
  3. RotationMatrix[x1, {y1, y2, y3}].({1, 1, 0}/Norm[{1, 1, 0}]) == {0, 1, 0},
  4. RotationMatrix[x1, {y1, y2, y3}].({-1, 1, 2}/
  5. Norm[{-1, 1, 2}]) == {0, 0, 1}}, {x1, y1, y2, y3}]
  6.  
  7. Solve[{EulerMatrix[{y1, y2, y3}].({-1, 1, -1}/
  8. Norm[{-1, 1, -1}]) == {1, 0, 0},
  9. EulerMatrix[{y1, y2, y3}].({1, 1, 0}/Norm[{1, 1, 0}]) == {0, 1, 0},
  10. EulerMatrix[{y1, y2, y3}].({-1, 1, 2}/Norm[{-1, 1, 2}]) == {0, 0, 1}},
  11. {y1, y2, y3}]
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