To find \( \theta \) given \( \sin(\theta) = 0.8660 \), we can use the inverse sine function, also known as arcsine.
\[ \theta = \arcsin(0.8660) \]
Using a calculator, we can find the value of \( \theta \).
\[ \theta \approx \arcsin(0.8660) \approx 60^\circ \]
Therefore, \( \theta \) is approximately \( \boxed{60^\circ} \).
