If you are given two 'line to neutral' sources of the same voltage but arbitrary phase difference (think 'wye' connection, but random angle rather than fixed 120 degree phase angle) and want to calculate the 'line-line' voltage, then you use 2*sin(angle/2). For small angles this value is pretty similar to sin(angle), but from 120 to 180 degrees (where the answer is that line-line = 2x line-neutral) you will see why you need 2*sin(angle/2)
-Jon
I'm not sure I follow this. Wouldn't you just subtract the two 230deg phasors seperated by 30deg similar to how you would phases of the same suource seperated by 120deg?