Cops can totally do that. "Entrapment" is actually quite narrow. IANAL, but my understanding is it requires showing that you wouldn't have done the illegal act

Cops can totally do that. "Entrapment" is actually quite narrow. IANAL, but my understanding is it requires showing that you wouldn't have done the illegal activity without the involvement of the police. Harassing a person for months to buy weed qualifies; posing as a drug dealer and offering drugs to the people who pass by you, does not.