Combine cake mix, reserved juice, egg whites and oil. Blend with an electric mixer on medium speed for 2 minutes, until creamy. Fold in oranges; pour into a greased and floured 13"x9" baking pan.
Bake at 350 degrees for 25 to 35 minutes, until a toothpick in the center comes out clean. Place pan on a wire rack to cool completely.
Pour pineapple and its juice into a medium bowl; stir in pudding mix. Fold in whipped topping and 1/2 cup coconut. Mix well; chill while cake is cooling. Spread over top and sides; sprinkle with remaining coconut. Serve immediately or keep refrigerated.