Now that it has been determined which sums and portions must be 0, along with sufficient relationships between the 10 components of the system, more substitutions are made to show requirements on the ratio of the sine and cosine sums.

A key technique in this section is to employ the fact that if 2 values are both 0, then their sum and difference must both be 0.

The result is a system of 2 equations and 2 unknowns that contains no sums, but that is based on the requirements on the constants from the even sums.