Ryan's Sines and Cosines

Algebra Level 3

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

${\sin^6 \theta}+{\cos^6 \theta}$

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

This problem is posed by Ryan P.

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