OK PSA because of math. An egg shell is about 2.5g of Calciumcarbonate. Calciumcarbonate is about 30% Calcium. So 1 egg shell is about 800mg of Calcium. This goes into megadosing territory and you might have calcium toxicity.
1/10th is 80mg calcium, enough for the optimal 1:2 phosphor:calcium ratio.
So put 1/10th of an egg shell into your coke.
This is a purely chemical reaction due to the acidity of the coke. Grinding, mixing, etc., has no effect. A whole egg shell takes about two days to dissolve, but 1/10 should just be a few hours.