=-sin[ (two-thirds faction+α)+(two-thirds faction-β)]

Because cos (three-thirds +α)=-3/5,

Sin(2/3 pie-beta)= 5/ 13, and 0

So the three-thirds system

So sin (three-thirds +alpha) =4/5.

Similarly, cos (two-thirds pie -beta) = 12/ 13.

So sin(β-α)=-sin(α-β)

=-sin[ (two-thirds faction+α)+(two-thirds faction-β)]

= - (4/5* 12/ 13-3/5*5/ 13)

= - 33/65