By Richard Cowan and Doina Chiacu WASHINGTON (Reuters) – U.S. Senator Kyrsten Sinema of Arizona is leaving the Democratic Party to become an independent, she said on Friday, just days after Democrats won a Senate race in Georgia and secured 51 seats in the 100-member chamber riven by deep political divisions. “Like a lot of Arizonans, I have never fit perfectly in either national party,” Sinema said in an article for the Arizona Republic newspaper. An aide would not say whether Sinema would continue to caucus with Democrats. Sinema herself, however, said she would not caucus with the Republica…