设：arccos1/3=a,arcsin2/3=b
则：cosa = 1/3,sinb = 2/3
所以,sina = 2√2/3,cosb = √5/3
sin（arccos1/3-arcsin2/3）
=sin(a-b)
=sinacosb-cosasinb
=(2√2/3)×(√5/3)-(1/3)×(2/3)
=（2√10-2）/9