As I would read it, the "may" or the "shall" are both only after the prerequisite "at the request in writing of the majority of the Broad of Directors". As I read it, it requires the request, in writing, of the majority of the board, before the meeting could be called. There is no special provision for not taking into account the vote of the director in question, so it would still require a request, in writing, by three of the members of the board. I am not sure if Delaware law supersedes my best guess on what this phrase means.