Expressed in terms of sin3θ, the value of si$n^3$θ is:

Start from sin3θ = 3sinθ − 4si$n^3$θ and make si$n^3$θ the subject: 4si$n^3$θ = 3sinθ − sin3θ, so si$n^3$θ = (3sinθ − sin3θ)/4. Check at θ = 30°: $(3\times 0.5$ − sin90°)/$4=(1.5-1)/4=0.125=(1/2{)}^3$.