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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