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Chop the grapefruit into small chunks and put them into a saucepan along with the orange slice, sugar, 125ml water, the cardamom pods and coriander seeds. Heat the mixture until simmering and cook for around 5 mins, crushing the fruit pieces with the back of a wooden spoon as it starts to soften to release the juices. Once the fruit has softened and the white pith has faded, take it off the heat and leave to cool. If you like you can add a splash of red food colouring to the syrup at this point.
Once the syrup mixture has cooled, strain it and discard the spices and fruit pieces. Fill a tumbler with ice and pour in 25ml of the syrup, the grape juice and 25ml cold water. Stir gently until the outside of the tumbler feels cold, then garnish with a slice of orange, if you like.