Volumes for twist link cone-manifolds

Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the 3-sphere and the singular set is the knot $4_1$ and the links $5_1^2$ and $6_2^2$, have been obtained by the second named author and his collaborators. In this paper we explicitly find the hyperbolic volume for cone-manifolds with the link $6_3^2$ as singular set. Trigonometric identities (Tangent, Sine and Cosine Rules) between complex lengths of singular components and cone angles are obtained for an infinite family of two-bridge links containing $5_1^2$ and $6_3^2$.