He tried to take a photograph of a beautiful butterfly which was flying past his left ear.
or
He tried to take a photograph of the beautiful butterfly which was flying past his left ear.
Also, is "which was flying past his left ear" a restrictive or non-restrictive clause in this sentence? I feel like it could be presented either way. Can please somebody clarify these 2 points (a/the and restrictive/non-restrictive) in this particular case.