This is the 2838th most frequent Korean word.
자유롭고
"Free" or "liberated."
In this sentence, '자유롭고' describes an attribute of the 'life' the subject wishes to have, coupled with '행복한' to depict desired qualities.
그는 자유롭고 행복한 삶을 살고 싶어 한다.
He wants to live a free and happy life.
Here, '자유롭고' attributes 'freedom' to the 'days', indicating a state of being unfettered.
자유롭고 걱정 없는 날들을 기다리고 있어요.
I'm looking forward to free and worry-free days.
In this use, '자유롭고' describes the landscape's mood or appearance as perceived from the painting.