  Let k be a global field and L be a finite dimensional \'etale algebra over k.
In this paper, we assume that L is a product of cyclic extensions of k. Let
T_{L/k} be the multinorm-one torus defined by the multinorm equation: N_{L/k}
(t) = 1. Let X_c be the variety defined by the equation N_{L/k} (t) = c, for
some c in k*. In this paper, we compute the Tate-Shafarevich group and the
algebraic Tate-Shafarevich group of the character group of T_{L/k}. These
groups measure the obstruction to the local-global principle for existence of
rational points of X_c and the obstruction to the weak appraximation.
