A child of mass $m$ stands on a swing's seat, with their CM at distance $\ell$ from the pivot. The child is held at angle $\theta_0$ from vertical and released from rest. As they pass through the lowest point of the swing, they instantaneously pull themselves up so that their CM is now at distance $\ell' < \ell$ from the pivot. To what maximum angle $\theta_1$ from vertical does the swing rise on the opposite side? Treat the pull-up as instantaneous, neglect the change in the child's moment of inertia about their CM, and assume the rope remains taut throughout. Express your answer in terms of $\theta_0$, $\ell$, and $\ell'$.