Once this is done,

The first spreadsheet reveals a couple of substitutions which might be helpful. The entire spreadsheet is available, but here are some the equations which motivate the next substitution.

The expressions with unknown variables

and knowns

There is nothing special about this category except for the appearance of the factor .

If we substitute a new variable for this term, then the equation above will be simplified somewhat, and perhaps several others will also. With a little foresight we will choose the variable

The expressions with unknown variables

and knowns

The factor appears in both of these categories. In the above category, the transpose of this term also appears, while in the category below, the term appears with an extra

The expressions with unknown variables

and knowns