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.