Solution
= Solution
The values of the <complex logarithm> at $-1$ are $i(2m+1)\pi$, $m\in\mathbb Z$. For any such value and any <integer> $n$,
$$
-i(2n+1)\log(-1)=(2n+1)(2m+1)\pi.
$$
This is an integer multiple of $\pi$, so its <sine> is zero. In particular the result holds with the principal value $\log(-1)=i\pi$. The argument does not require treating the multivalued logarithm as a single globally defined function.