When any city or town is contiguous to any city existing under any special charter of this state or the territory of Colorado, which charter was issued prior to July 3, 1877, and in such special charter it is provided that when any such city or town, in pursuance of any law of this state, is dissolved or becomes annexed to the city existing under a special charter and the area included within such city or town existing under general laws becomes part of the city existing under a special charter, the city or town may be annexed to and become part of the city existing under a special charter in the manner set forth in this part 3.