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You should fill it about halfway, if not a little higher. A simple syrup is nothing more than a combination of equal parts granulated sugar and water, heated together until the sugar dissolves. Simple syrups are great for reducing the bitterness of alcohol and extremely sour juices. Pour all three liquids into your shaker and over the ice before securing the cap. The ice in the shaker not only cools the cocktail but also helps to combine the syrup into the alcohol and the juice. Continue shaking using your dominant hand, pointing the lid of the shaker away from you and anyone else, for 15 to 30 seconds. The strainer built into your shaker should suffice, but you can also double-strain your gin sour by pouring the liquid through a separate cocktail strainer, as well.

Summary:
Fill the shaker with ice. Pour the gin, lemon juice, and simple syrup into the shaker. Shake vigorously. Strain the drink into a cocktail glass.