原题应该是：it's required that no smoking____in the theatre.
其中,it是形式主语,后面的从句that no smoking____in the theatre是真正的主语（从句）,因为require后面的宾语从句必须采用虚拟语气,所以变成被动后即be required的主语从句也必须采用虚拟语气.
其构成为从句的谓语动词采用“should + 动词原形”构成,其中should可以省略.
即：that no smoking be permitted in the theatre
= that no smoking should be permitted in the theatre