Having the strongest taste of tang, which is a sharp, strong flavor like the taste of a lemon or a pickle.
The word tangiest makes people think of very strong flavors, like sour or sharp tastes.
Examples:
This lemon is the tangiest one I've ever tasted.
The tangiest part of the salad was the pickles.
She made the tangiest soup I've ever had.
The tangiest candy made my mouth pucker!
The tangiest fruit in the world is the miracle berry.
The tangiest drink I've ever had was a sour lemonade.