=-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