Bring egg whites to room temperature (about 1 hour).
Meanwhile, sift flour, powdered sugar, cocoa powder, and cinnamon together three times.
In a large mixer bowl beat the egg whites, cream of tartar, and vanilla with an electric mixer on medium speed till soft peaks form (tips curl).
Gradually add the sugar, 2 tablespoons at a time, beating on high speed till stiff peaks form (tips stand straight).
Transfer to a larger bowl, if necessary.
Sift about one fourth of the flour mixture over the beaten egg whites; fold in gently.
Repeat, folding in the remaining flour mixture by fourths.
Pour into an ungreased 10 inch tube pan.
Bake on the lowest rack in a 350° oven for 40 to 45 minutes or till top springs back when lightly touched.
Immediately invert cake (leave in pan); cool thoroughly.
Loosen sides of cake from pan; remove cake.
Slice into 16 wedges.