"Cap over the windmill" is an idiom used to describe an unnecessary and futile action, as the windmill's cap is already in place and there is no need to try to put it on top. There are various synonyms for this phrase, including "reinventing the wheel," which means wasting time and resources by trying to create something that has already been done; "adding fuel to the fire," which means making a bad situation worse by taking an unnecessary action; and "beating a dead horse," which refers to continuing with an action or argument that is already over. All these synonyms highlight the importance of avoiding unnecessary actions and focusing on what is essential.