An agreement of compromise made pursuant to § 12-372 shall fix the amount to be accepted in full satisfaction of the tax imposed by this chapter, including any interest to the date of filing the agreement, and shall likewise fix the amount to be accepted by the other state or states in full satisfaction of the death taxes thereof. The amount fixed in such agreement shall finally determine the amount of the tax imposed by this chapter without regard to any other provision of the laws of this state. If a tax would have been imposed upon the transfer of the decedent‘s estate under the provisions of chapter 217 if he had died domiciled in this state, such agreement shall also fix the amount to be accepted in full satisfaction of the tax imposed by said chapter, including any interest to the date of filing the agreement, and the Commissioner of Revenue Services shall determine and assess the tax imposed by said chapter at the amount fixed in such agreement and such determination and assessment shall finally determine the amount of the tax imposed by said chapter, without regard to any other provision of the laws of this state.