In a small bowl combine the 1 cup toasted coconut, ground pecans, and melted margarine or butter. Press into the bottom of a 9-inch springform pan. Set aside.
In a large mixer bowl beat cream cheese with an electric mixer on low speed; gradually add the 1/2 cup sugar, first 1/2 teaspoon vanilla, and almond extract. Beat until fluffy. Add the 3 whole eggs; beat on low speed just until combined. Pour into crust-lined pan. Bake in a 350 degree F. oven for 35 minutes. (Cheesecake will not be completely done at this point.)
Meanwhile, in a small mixing bowl beat egg white and remaining vanilla with an electric mixer until soft peaks form (tips curl); gradually beat in the 1/3 cup sugar until stiff peaks form. Fold in the 2/3 cup toasted coconut. Carefully spread atop partially baked cheesecake. Return to oven and bake 20 minutes more. Cool on wire rack for 15 minutes. Loosen sides of cheesecake from pan. Cool 30 minutes more; remove sides of pan. Cool completely. Cover and chill at least 4 hours before serving. To serve, garnish with strawberries and additional toasted coconut, if desired. Makes 12 to 16 servings.