  Recently Feher and the author have constructed the action-angle dual of the
trigonometric BC(n) Sutherland system via Hamiltonian reduction. In this paper
a reduction-based calculation is carried out to verify canonical Poisson
bracket relations on the phase space of this dual model. Hence the material
serves complementary purposes whilst it can also be regarded as a suitable
modification of the hyperbolic case previously sorted out by Pusztai.
