Place water, egg whites, granulated sugar, brown sugar, and cream of tartar in the top of a double boiler or a water bath pan. Place over boiling water (bottom of upper pan should not touch water). Cook, beating with an electric mixer on high speed about 7 minutes or until frosting forms stiff peaks, scraping sides of pan occasionally. Remove from heat; add vanilla and coconut extract. Beat for 2 to 3 minutes more or until frosting is spreading consistency. Fold in 1/4 cup of the coconut. Sprinkle remaining coconut on frosted cake. Makes 3-1/2 cups.