The three rotation angles represent rotation about each of the three axes. The scaling and rotation angles are, usually, very small. Therefore, it has become common practice to specify rotation angles in seconds of arc. General rules of right handed coordinate systems apply and control the direction vs. sign of the angle issue which is beyond the scope of the Casual Cartographer. Again, the trial and error procedure is often used by the Casual Cartographer.
Scale factors are also very small.
That is, a scale specification of -4.234 produces a scale factor of 0.999995766. Often one needs, or desires, to match existing numbers precisely. For example, when evaluating a software product, or when attempting to figure out which datum a specific data set is based on. Given a reasonable number of points at which both the source datum and the target datum coordinates are known, mathematical techniques can be used to develop analytical formulas which can convert between the two datums. A general term for such techniques is regression analysis, or when applied to more than one dimension, multiple regression analysis.