Existence, Uniqueness & Bifurcations · Superchallenge problem

Let $y(t; y_0)$ denote the solution of $y' = \sin y$ with $y(0) = y_0$. How sensitive is the solution to its starting value? Find $\dfrac{\partial y}{\partial y_0}$ at $t = \ln 3$ and $y_0 = \dfrac{\pi}{2}$. Express your answer as a common fraction.