SolveAConjugatePairOfImaginaryTangentSums​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

Powers of the two conjugate sums a + i a tan(z) and c - i c tan(z), not both
whole and adding up to a whole number k, beside a function of the tangent, the
secant or the cosine of the same argument, integrated as the exponential they are:
a + i a tan(z) is a sec(z) e^(i z) on the real line and
c - i c tan(z) is c sec(z) e^(-i z), so the pair is a constant on every
interval where it is continuous times sec(z)^k e^(i (p - q) z), and in
w = e^(i z) the whole is a rational function of w times a power of it.