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In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω\Omega of the CR manifold S3{{\mathbb{S}}}^{3} bounded by the Clifford torus Σ\Sigma is discussed. The Yamabe-type problem of finding a contact form on Ω\Omega which has zero Tanaka-Webster scalar curvature and for which Σ\Sigma has a constant pp-mean curvature is also discussed.