Japan PM seeks to regain public's trust after Tokyo poll setback

By Linda Sieg and Kaori KanekoTOKYO (Reuters) - Japanese Prime Minister Shinzo Abe said on Monday he will work to regain public trust after his party suffered an historic defeat in an election in the nation's capital, signaling trouble ahead for the premier amid tumbling support rates.The dismal showing for Abe's Liberal Democratic Party (LDP) in Sunday's Tokyo Metropolitan assembly election was a stinging rebuke for his 4-1/2-year-old administration, although on the surface it was a referendum