Show that the function sine assigns the same value to each element of any fixed left coset of the subgroup (2) of the additive group

Show that the function sine assigns the same value to each element of any fixed left coset of the subgroup (2π) of the additive group R of real numbers. (Thus sine induces a well-defined function on the set of cosets; the value of the function on a coset is obtained when we choose an element x of the coset and compute sin x .)