If you have N equations in N variables, then asking to solve for fewer than N variables will almost always tell you that no solution could be found.
In your second expression you need to fix the con(pa) to cos(pa)
What are you going to do with the large number of solutions over the imaginaries?
What are you going to do about the fact that sub-solutions to this problem involve polynomials which to any fixed numeric precision evaluate as having imaginary roots, but in the infinite precision limit the roots are completely real?
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