Coconut Rim: Place your shredded coconut on a small plate. Grab your glass and moisten the rim with the lime. Place your glass upside down into the coconut to stick the coconut onto the rim of the glass. Set aside.
Margarita: In a cocktail shaker, add a few ice cubes, coconut milk, coconut cream, lime juice, tequila, triple sec, and lime juice. Shake for about 30 seconds, until you feel the shaker become well chilled.
Fill your glass ⅔ full with ice and strain your cocktail into the glass. Garnish with mint, lime slices, or extra coconut, as desired, and serve immediately.