A Cook County jury ordered the city of Chicago to pay $3 million to the family of a woman who was strangled to death a day after police failed to detain her live-in boyfriend for allegedly threatening her with a samurai sword and a butcher knife.The award in favor of Vanessa Taylor’s estate is the highest under the Illinois Domestic Violence Act of 1986 that the Jury Verdict Reporter has reported.A 12-member jury in Cook County Associate Judge Israel A. Desierto’s court returned the verdict on Thursday.The lead attorney …