Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we propose the Bethe ansatz solution for the transfer matrix eigenvalues for cases where atmost two of the boundary parameters are set to be arbitrary and the bulk anisotropy parameter has values \eta = i \pi/3, i \pi/5,... We present numerical evidence to demonstrate completeness of the Bethe ansatz solutions derived for s = 1/2 and s = 1.