α ,180K+30＜α＜180K +90等价于360k＋30＜α＜360k+90,
且180（2K＋1）+30＜α＜180（2K＋1）＋90,即360k＋210＜α＜360k+270
故A={α|360k＋30＜α＜360k+90且360k＋210＜α＜360k+270k∈Z}.
β ,360k+315＜β＜360k+405,即360k+315＜β＜360k＋360
且360k＜β＜360k+45
故B={β|360k＜β＜360k+45且360k+315＜β＜360k＋360k∈Z},
A∩B={θ|360k＋30＜θ＜360k+45,k∈Z}.