Transcription: 양국간 공조를 배경으로 하고 있습니다.
Translation: The agreement was made under the premise that the two countries would cooperate.
Although this clause is stated using the present tense 하고 있습니다, it mentions the previous FTAs. Therefore, make sure to translate with the past tense.
공조(共助) comes from 공동협조 meaning "mutual help or cooperation."
Transcription: 미국은 경제와 안보 관계를 동시에 추구하는 정책을 띠고 있습니다.
Translation: The U.S. is seeking a policy that will advance both its security and economic interests.
Here, the verb 띠다 in 정책을 띠다 means 보이다, or 나타내다.
Transcription: 9.11사태 이후 반테러 정책을 확대해 가는 과정에서
Translation: In expanding its antiterrorism policy since Sep 11
Frequently used phrase -하는/해 가는 과정에서 means "going through a process of."
Transcription: 외교적 차원의 복합적 동맹망을 구축하려한다
Translation: Try to establish a network of diplomatic combined alliances.
As explained in the Teacher's Note of Activity 2, the phrase -적 차원의, is frequently used in higher levels and means "in terms of."
구축하다 which means 바탕을 닦아 이루거나 마련하다 is used as in 정치적 기반을 구축하다 or 진지를 구축하다.