I just want to add that 도 isn't just to say "too", "as well", "either/neither", "nor", it is also a particle for "even if".
For example:
설령 그녀가 오지 않더라도 나는 개의치 않겠어요 (I won't mind even if she doesn't come.)
싫더라도 꼭 해야 돼요. (Even if you don't like it, you must do it.)