The stuff i read tends to tar all types of sodas with the same brush, and that is terribly inaccurate. The anti-soda gang doesn't like any of them and generally says anything other than water is gonna kill you. However, chemical content differs widely with the type of sweetener used, flavorings, etc., so the negative effects often cited may or may not apply.
Coke Zero uses aspartame as the sweetener. That' the same ingredient as in NutraSweet and Equal. The FDA says that adults should not exceed 50 mg os aspartame per kilogram (2.2 lbs) of body weight. A typical can of diet soda contains about 185 mg of aspartame, so a 150 lb person could consume up to about 18 cans/day. The EFSA suggests a lower limit, 40 mg/kg or about 15 cans of aspartane-based diet soda per days. You are consuming an average of 3 cans of Coke ero per day, so I'll leave it for you to decide.
I would encourage you not to get too focused on any one ingredient, or any one source. Consider your overall diet and the amounts, types, and times you consume foods and beverages.
By the way, if you want to stay pure, that bottled water you are consuming contains some extra chemicals too. Most have 2-4 salts of various types, e.g. calcium chloride, potassium chloride, and magnesium sulfate. Before you get too upset about that, natural ground water usually contains several minerals and salts as well. "Pure" water is a rarity, whether in nature or municipal water supplies.