Peel shrimp, leaving tails intact. Starting at tail end, butterfly each shrimp, cutting to, but not through, backside of shrimp.
Combine breadcrumbs and next 3 ingredients in a shallow bowl. Beat egg whites with a whisk until foamy in a separate bowl. Add half of shrimp to egg whites, tossing to coat. Dredge shrimp in coconut mixture, pressing gently to adhere. Place shrimp on a parchment paper–lined baking sheet. Repeat procedure with remaining shrimp, egg whites, and coconut mixture.
Bake at 425° for 6 minutes. Using tongs, grasp shrimp by tails and turn over. Bake an additional 6 minutes or until golden brown. Serve shrimp with Mango Sauce.