1) 다른 사람이 너를 어떻게 보는지는 중요하지 않다. 2) 네가 어떻게 보는지가 가장 중요하다. Actually, ..보는지 is already a noun phrase(noun clause) even without 는 or 가. Attaching 는 or 가 adds a connotation and makes the sentence smoother. The particle is not always necessary but these examples sound a bit abrupt without it. In #1, 는 adds the sense "... isn't important itself (but something else is)", then #2 supplies that important thing. This is one of the common ways that 은/는 and 이/가 work together, similar to "... not that ... but that ...". Also, ~지 makes a noun from a verb/adjective, often (but not always) used to express the sense of "whether". It is not as universal as "~ 것", but still widely used when you want a lighter construction. Compare these examples: 1. 왜 이렇게 바쁜지 모르겠다: I don't know why I am so busy. 2. 왜 이렇게 바쁜 것인지 모르겠다: (same) * The two are similar but #2 stresses the fact(a bit overly elaborate). #1 feels lighter and smoother. 1. 바쁜 것은[이] 꼭 나쁜 게 아니다: It is not necessarily a bad thing to be busy. 2. 바쁜지는 꼭 나쁜 게 아니다: BAD. ~지 has a limited application. Only 바쁜 것 can work here. * ~지 is used when "whether/if" or "why" is implied, so not appropriate when introducing a new, independent fact.