Preheat the oven to 275°. Line a baking sheet with parchment paper and lightly spray it with cooking spray. In a large bowl, using an electric mixer, beat the egg whites with the cream of tartar at medium speed until frothy. Beat in the sugar, 1 tablespoon at a time, until the meringue is thick and glossy. Beat in the vanilla extract, then fold in the shredded coconut.