The question is well defined for estimating $\frac 1 \pi$, but not for estimating $\pi$. In the first case, minimize the variance of the estimator of $\frac 1 \pi$, it will give you $\frac{2l^*}{d\pi} = \frac 1 2$.

The question is well defined for estimating $\frac 1 \pi$, but not for estimating $\pi$. If $l>d$, you need to evaluate $cos^{-1}$ which requires knowledge of $\pi$, otherwise the variance of the estimator decreases with$ \frac l d$, so you'd "practically" settle for $l=d$.