If sinθ = 1/3, then the value of sin3θ is:

The triple-angle form is sin3θ = 3sinθ − 4si$n^3$θ = $3(1/3)-4(1/27)=1-4/27=23/27$ ≈ 0.852. Treating sin3θ as 3sinθ gives the trap 1, reversing the identity to 4si$n^3$θ − 3sinθ gives −23/27, and adding instead of subtracting gives 31/27.