There is no way to answer that. Can you tell me how long it will take to learn Japanese? it varies with the person. Some people are more naturally flexible, therefore it would not take as long as with someone less naturally flexible.
My question to you is why does it matter how long it takes? If you are in a good school you will be at least 4 years in getting a black belt. I know TKD black belts that have never reached 180 degree stretch, fact is it doesn't matter. It will take as long as it takes. No class worth going to is going to limit you because you don't have a 180 degree stretch. Yes TKD stresses the need for head level kicks, but for the most part that doesn't require 180 degree stretch.
Attend classes, stretch everyday and don't worry about when or if you ever get that 180 degree stretch.
