sin(α +β )=sinαcosβ +sinβcosα =1/2,
sin(α -β )=sinαcosβ -sinβcosα =1/3,
解得 sinαcosβ = 5/12 sinβcosα=1/12
tanα*cot β
=sinαcosβ /sinβcosα
=5/12/1/12
=5
那么M=log√5(tanα*cot β)²
=log√5(√5)^4
=4.