(Solved): Use the appropriate reciprocal identity to find the exact value of \( \sin \theta \) for the given ...

Use the appropriate reciprocal identity to find the exact value of \( \sin \theta \) for the given value of csc \( \theta \). Rationalize denominators when applicable. \[ \csc \theta=\frac{\sqrt{117}}{2} \] \( \sin \theta= \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)