First of all, precision of 1e-8 is ok to get AC (with double type and without trigonometry).

Now about WA16 - that's the case when one of boundary rays is parallel to OX. When some angular segments crosses OX, I perform a split at 0/2PI point. In described case it was possible that I first delete a draught at point 0 and then add it. So, sorting should be not just angular, but also additions should precede deletions. This condition is automatic for regular cases, so I omitted it. But in described case special care should be taken.