L.A. County’s unemployment rate in February was 4.5 percent, unchanged from January amid broad-based job gains for the month, according to state figures released Friday. The unemployment rate was below the 4.9 percent level of a year ago, the state Employment Development Department reported. But it was higher than the statewide average of 4.3 percent and the national average of 4.1 percent. The rate stayed steady as a slight drop of 2,000 employment positions among county residents was offset by a slight drop of 2,000 in the labor force to 5.14 million. Los Angeles, the county’s largest city, reported an unemployment rate of 4.5 percent. The city with the highest rate was Lancaster at 6.7 percent. Rates in some unincorporated communities were as high as 8.4 percent. Nine of the 11 broad industry sectors reported job gains over the month, led by the entertainment sector (motion picture and sound recording), which added a net 10,500 jobs. Other gainers included leisure/hospitality (up 9,000 jobs) and construction (up 4,000). The only sector to post major job losses in February was trade/transportation/utilities, down a net 13,500 jobs. The lion’s share of that drop was in retail stores, which shed 10,400 jobs.