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Set aside one of the lime wedges, then squeeze the juice from the rest into a tall glass. Drop in the spent lime wedges and muddle using a muddler or the end of a rolling pin.
Set three of the mint leaves aside, then drop the rest into the glass along with the sugar syrup. Fill the glass with crushed ice, then pour over the rum. Stir upwards from the bottom using a long-handled spoon to evenly disperse the lime juice and mint.
Top up the glass with golden ale, then garnish the rim with the remaining lime wedge and scatter over the rest of the mint leaves.