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2 sin(z) + cos(z) = i sin(z)

2((exp^iz - exp^-iz)/2i) + (exp^iz + exp^-iz)/2 = i((exp^iz - exp^-iz)/2i)

2(exp^iz - exp^-iz) + i(exp^iz + exp^-iz) = i(exp^iz - exp^-iz)

exp^iz - exp^-iz = -i exp^-iz

let u = exp^iz

u - 1/u = -i/u

u^2 - 1 = -i

u = (1 - i)^(1/2)

exp^iz = (1 - i)^(1/2)

iz = ln((1 - i)^(1/2))

iz = (1/2)ln(1 - i)

iz = ((sqrt 3)/2)(ln(sqrt 2) - ln(2))