Extension of the Phragmén-Lindelöf Theorem

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Above is the statement of the theorem. And below is the exercise I am stuck at. I think I have to figure out the extended boundary of V∩G and apply the original theorem to V∩G. However, I can't figure out the extended boundary of V∩G at all.... Could anyone please help me how to extend the Phragmén-Lindelöf Theorem?

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