Ryan's Sines and Cosines

Algebra Level 3

Given that sin(2θ)=23 \sin (2\theta) =\frac{2}{3}, the value of

sin6θ+cos6θ{\sin^6 \theta}+{\cos^6 \theta}

can be written as ab \frac{a}{b} with aa and bb coprime positive integers. Find a+b a+b.

This problem is posed by Ryan P.

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