The board of trustees of the district shall provide for the appointment of a board of adjustment, shall provide that the board of adjustment may, in appropriate cases, and subject to appropriate conditions and safeguards, make special exceptions to the terms of the land use plan which are in harmony with its general purpose and intent and in accordance with the general or specific rules of the plan, and provide that a property owner aggrieved by the action of the board of trustees in the adoption of the land use plan may petition the board of adjustment directly to modify regulations and restrictions as applied to those property owners.