Probably shouldn't shoot it, woodpeckers are protected and shooting them is a felony... at least in this country.
This is what's recommended around me:
http://www.in.gov/dnr/fishwild/files/fw-Nuisance_Bird_Info_Woodpeckers.pdf
I was speaking to my neighbors about something similar. They had a pecker start hitting their aluminum drain pipe and it rattled through the whole house. They put a owl statue near the pecking area and it immediately stopped.
And then tigers will get rid of the lions.
