Carbonated Beverages and Atmospheric CO2

I recently issued an essay concerning the position of the National Research Council (NRC) on global warming, or if it's rather cold, climate change.
The NRC says there is too much carbon dioxide in the atmosphere and that such excessive amount causes global warming or climate change. There are a couple of difficulties with that position. First of all, there is no clear connection between atmospheric carbon dioxide concentration and climate. We know that the total presence of atmospheric gases tends to equalize temperatures between night and day on the Earth surface, so that Earth is livable. However, the atmospheric concentration of carbon dioxide is only 0.05%, which does not make a significant contribution to the total.
The other question is "how much is too much"? The NRC ignores that, but touches lightly on it in mentioning photosynthesis.
The new factor is that after issuing my essay, one of our political constituents asked whether carbonated beverages have an effect.
First of all, I claim that any concentration of carbon dioxide in the atmosphere below say 10% will have no effect on climate. Although not normally considered climate, the difference between night and day Earth surface temperatures is a very significant portion of climate and is controlled mainly by the major gasses of the atmosphere, which are nitrogen and oxygen.
But for discussion, let's say I am wrong and carbon dioxide has unusual properties in affecting climate. Starting from that basis, let's take a look at the contribution of carbonated beverages.
Annual world production of carbonated beverages is 188 billion liters. A 12-ounce (355 millititers) can of Coca-Cola contains 2.2 g of CO2. That 6.2 g of CO2 per liter of carbonated drink or 1166 billion grams of CO2 in the annual world production. That is also 2.6 x 10^6 US tons (i.e. 1.17 X 10^12 / 1 X 10^6 X 2.2) of CO2.
The mass of the Earth's atmosphere is 5.6 x 10^17 US tons. At 0.05% CO2, the atmospheric mass of CO2 is 2.8  X 10^14 US tons.
Let's assume that all CO2 content of the annual world production is lost to the atmosphere through opening the containers and belching. Therefore, the annual addition of CO2 to the atmosphere from carbonated beverages is 2.6 x10^6 / 2.8 x 10^14 x 100 = 0.000001%. After 10 years, the addition of CO2 to the atmosphere would have been 0.00001%.
For those who want to have skipped the calculations, and assume that I have made no mathematical errors, the answer to the political associate's question of whether carbon dioxide in carbonated beverages makes a significant difference to the CO2 content of the atmosphere, the answer is "no".