First, I'm not sure on which level どうすれば stands in the hierarchy of the sentence. I would say that it doesn't belong to この地球から戦争を無くすことが I would say that it is on the top level of the sentence... "How to do/What to do, so that..."
Second, I guess the subject of the part
can only be realized through the indefinite personal pronoun "one": "What to do, so that one can remove war from this globe."
Third, I have problems in understanding how どうすれば and のだろうか work together here. どうすれば asks for a method, while のだろうか shows that the speaker wonders about X. のだろうか was just introduced in my textbook and the archetypal examplephrases usually contained stuff like: "What might I have to do in order to get that job". I hope this somehow reflects in english what I was taught in german ^^ I'm german and I'm using a german textbook, so this was just a guess on how to translate the example in my textbook into english ^^
Now concerning the sentence in question, I feel like I'm missing out on something, because I feel like I have to drop one of the two to get a sentence that still makes sense．
"What to do so one might be able to remove war from this globe"
doesn't seem wrong to me, but I feel quite weary about it because it gives off the impression that the speaker doesn't really believe into the feasibility of this. This might be correct, but since this would be a very distinct meaning, I'd rather have someone confirm that it's either right or wrong before I believe into my understanding of this sentence^^