Initial situation: I have a world coordinate system in 3D space. The initial coordinate system is like the world coordinate system. The unit vectors are x: (1,0,0); y: (0,1,0) and z: (0,0,1). Problem statement: The z-unit vector of a rotated coordinate system (i call it rot_cs) is now given. I now want to know by how many degrees | have to rotate the initial coordinate system in the rotation order Y-X-Z around the axes of the world coordinate system in order to get the initial vector z (0,0,1) to the z unit vector of the rotated coordinate system.

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