[subject] + 在一定程度上 + [verb phrase]
在一定程度上 + ,+ [clause]
[subject] + 在很大程度上 + [verb phrase]
在一定程度上 makes a claim partial: true, but not the whole story. 一定 here means "a certain", not "definitely". The phrase goes after the subject and before the verb, like other adverbials, and belongs to essays, reports and papers.
It can also open the sentence, followed by a comma.
在很大程度上 raises the degree, "to a large extent", "largely".
In writing 在 is often dropped: 一定程度上, 很大程度上.
English puts "to some extent" at the end of the clause. Chinese keeps it in front of the verb.