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Good news! A rotation matrix is a rotation matrix is a rotation matrix. A rotation can be represented by several different conventions of euler angles, ex, the Z-X-Y, ect. However, if they represent the same rotation, the produce the same rotation matrix. It is different matrices multiplied together in a different order, but the same end result.

What that means for you, is that you can decompose the rotation matrix to your heart's content without worrying about how the Rodrigues function works.