Any city of the first class in this state, is hereby empowered to exchange for other lands to be used for parks or playgrounds, any lands acquired by the city for parks or playgrounds; provided that at least two-thirds of all the members of its council shall approve such exchange and the board of park commissioners, or other body having jurisdiction and control of parks and playgrounds in the city, shall, by a two-thirds vote thereof, request the council so to do.