Sift flour, 3/4 cup sugar, cocoa, and cinnamon together 3 times.
Beat egg whites and cream of tartar in an extra-large bowl with a mixer at high speed until foamy. Gradually add remaining 1/4 cup sugar, beating until soft peaks form. Sift flour mixture over egg white mixture, 1 tablespoon at a time; fold in gently after each addition. Combine coffee granules and water. Fold coffee mixture and vanilla into batter.
Spoon batter into an ungreased 10-inch tube pan; spread evenly with a spatula. Break large air pockets by cutting through batter with knife.
Bake at 300° for 50 minutes or until cake springs back when lightly touched. Remove cake from oven; invert pan, and cool completely. Loosen cake from sides of pan, using a narrow metal spatula; remove from pan.