THREE.js rotating cylinders and fittings

This is a question regarding 3D rotation using THREE.js and predefined mesh models. All components originate on the <0,0,1> vector as shown on the image. I have no problem getting the cylinders rotated into the correct position. I can also get the fitting rotated to fit the receiving cylinder.  The problem is getting the inlet of the fitting rotated around its own Z-axis to meet the incoming cylinder. Note that the cylinders can be pointing in any direction and the angle between them can be anything from 15 to 90 degrees (using the appropriate fitting. Is it possible to have a single method to rotate the Z-axis regardless of angle?