Final answer:
The approval of surveillance rules by a judge for the NYPD likely occurred after both the lawsuit by Barbara Handschu and the terrorist attacks in the U.S., based on the context of increased governmental powers post-9/11.
Step-by-step explanation:
The sequence of events that the question refers to includes acts of governmental surveillance, legal challenges, and policy changes related to civil liberties in the United States. The specific events mentioned are not dated in the question, but based on historical context, it is possible to infer that the approval of surveillance rules by a judge for the NYPD's head of intelligence to act independently likely came after both the challenges by protesters like Barbara Handschu and the terrorist attacks mentioned.
After the terrorist attacks, such as those on September 11, 2001, the U.S. government took measures to tighten security and surveillance through laws like the Patriot Act. Consequently, a judge's approval to authorize independent surveillance by the NYPD's head of intelligence likely occurred in the context of increased security concerns. In contrast, the agreement by the NYPD to the rules barring surveillance based on religious or political leanings and the lawsuit by Barbara Handschu and other protesters predate these broader security measures.