Green tea cucumber

• cucumber simple syrup (makes 1 cup)
• 1 cucumber, sliced
• 3/4 cup granulated sugar
• 3/4 cup water
• green tea cucumber cocktail
• 3/4 cup light rum
• 1/2 cup lime juice
• 30 leaves fresh mint, muddle 
• 2 cups green tea, brewed, cooled
• 1 cup Cucumber Simple syrup 
• 1/2 cup club soda
• cucumber, sliced , for garnish if desired
• wedge lime, for garnish if desired