  For the potential function of a link diagram induced by the optimistic limit
of the colored Jones polynomial, we show the existence of a solution of the
hyperbolicity equations by directly constructing it. This construction is based
on the shadow-coloring of the conjugation quandle induced by a
boundary-parabolic representation $\rho:\pi_1(L)\rightarrow{\rm
PSL}(2,\mathbb{C})$. This gives us a very simple and combinatorial method to
calculate the complex volume of $\rho$.
