Coat 3 (8-inch) round cake pans with cooking spray; dust with 1 tablespoon flour.
Lightly spoon sifted flour into dry measuring cups, and level with a knife. Combine sifted flour, baking powder, salt, and baking soda. Combine sugar, butter, and oil in a large bowl, and beat at medium speed of a mixer until well-blended (about 5 minutes). Add egg whites, 1 at a time, beating well after each addition. Combine the milk and yogurt. Add the flour mixture to the creamed mixture alternately with the milk mixture, beginning and ending with flour mixture. Stir in extracts.
Pour cake batter into prepared pans. Sharply tap cake pans once on countertop to remove air bubbles. Bake at 350° for 25 minutes or until a wooden pick inserted in center of cake comes out clean. Cool in pans 10 minutes on wire racks, and remove from pans. Cool completely on wire racks.
To make frosting: Combine first 5 ingredients in top of a double boiler; place egg white mixture over barely simmering water in bottom of double boiler on cooktop. Beat at high speed of a hand-held mixer until stiff peaks form and candy thermometer registers 160°. Add extracts; beat until blended.
Place 1 cake layer on a plate; spread with 2/3 cup Fluffy Coconut Frosting, and top with another cake layer. Spread with 2/3 cup frosting, and top with the remaining cake layer. Spread the remaining frosting over the top and sides of the cake. Sprinkle top of cake with coconut. Store cake loosely covered in refrigerator.