1) Install authbind
2) Make port 80 available to authbind (you need to be root):
touch /etc/authbind/byport/80
chmod 500 /etc/authbind/byport/80
chown tomcat7 /etc/authbind/byport/80
3) Make IPv4 the default (authbind does not currently support IPv6).
To do so, create the file TOMCAT/bin/setenv.sh with the following content:
CATALINA_OPTS="-Djava.net.preferIPv4Stack=true"
4) Change /usr/share/tomcat7/bin/startup.sh
exec authbind --deep "$PRGDIR"/"$EXECUTABLE" start "$@"
# OLD: exec "$PRGDIR"/"$EXECUTABLE" start "$@"