Choose carefully between that, which, and who.
As a general rule, use that when a relative clause is restrictive (without a comma), which when a relative clause is non-restrictive (with a comma), and who in either case whenever the antecedent is a person.
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This is the main problem, which we must solve.
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This is the main problem that we must solve.
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She was wearing a coat, that was sky-blue.