In a (2-quart) heat-proof glass pitcher, add the tea bags to it. (If the tea bags have strings attached, be sure to remove them first.)
Pour boiling water over tea bags in the pitcher.
Cover the pitcher, and allow tea to steep for 45 minutes. (I covered the pitcher with Saran Wrap.)
After the has steeped for 45 minutes, remove tea bags from the pitcher, and discard them.
To the pitcher, add the 3/4 cup of sugar, plus the 2-1/2 tablespoons of sugar; stir thoroughly to dissolve the sugar.
Add the juice of 2 limes to the pitcher, and stir. (For more lime flavor, add the juice from half of a lime as well.)
Let the tea cool to room temperature, then place tea in the refrigerator to chill.
Pour chilled tea into glasses filled with ice. Serve tea immediately.
*Note: For more lime flavor, add the juice of 2 and a 1/2 limes. Also, I usually double this recipe, and make the tea in a gallon size glass jar. Then I'll use 12 cups of boiling water, 14 tea bags, 1-1/2 cups of sugar, plus a 1/3 cup of sugar, and the juice of 4 limes (possibly 4-1/2 limes). This makes: 13-1/2 cups of tea (or) 105-ounces. One more thing I wanted to mention, if using a gallon size glass jar to make the tea, I'll cover the jar with an 8-1/2 inch glass dinner plate, while the tea is steeping.