  Using the fermionic basis discovered in the 6-vertex model, we derive exact
formulas for the expectation values of local operators of the sine-Gordon
theory in any eigenstate of the Hamiltonian. We tested our formulas in the pure
multi-soliton sector of the theory. In the ultraviolet limit, we checked our
results against Liouville 3-point functions, while in the infrared limit, we
evaluated our formulas in the semi-classical limit and compared them upto
2-particle contributions against the semi-classical limit of the previously
conjectured LeClair-Mussardo type formula. Complete agreement was found in both
cases.
