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I want to get a haircut before the trip.
Literal
Trip [to-に] go-out before [time-に] head [object-を] cut [preparatory-ておきたい].
頭を刈る (to cut hair, literally 'to shear the head') is a somewhat old-fashioned or male-oriented expression — modern Japanese more commonly uses 髪を切る. ~ておきたい combines ておく (do in advance) with たい (want to) — 'want to get it done beforehand.'