considering you are on the same LAN segment i would use a tool like Dsniff(network sniffer and password extractor program ) let it run for a couple of days then check if you got some password your brother uses on other sites, then use a program like hydra (dictionary hacker program ), wright a pass file of all different combos of previously sniffed passwords and you might get lucky people tend to either use the same password on lots of places or different combinations or adding numbers and so on.
good luck and happy hacking.
i hope this is for purely education purposes