Position a rack in the middle of the oven and preheat to 350 degrees . Sift together the cake flour and confectioners sugar 3 times.
Using an electric mixer, beat the egg whites, cream of tartar, vanilla and salt until firm peaks form. Working in thirds, add 3/4 cup granulated sugar, beating for 5 seconds between additions. Beat on high speed until stiff, glossy peaks form, about 3 minutes. Working in thirds, gently fold in the flour mixture, then fold in the coconut. Scrape into a 10-inch angel food cake pan, smoothing out the top. Bake until golden and the center of the cake springs back to the touch, about 40 minutes. Invert the cake onto a rack or the neck of a bottle and let cool in the pan completely, about 1 1/2 hours.
Just before serving, whip the cream with the remaining 2 tablespoons granulated sugar. Serve the cake with the whipped cream and berries.