TOKYO — In a rare display of democratic muscle in this traditionally apolitical nation, Japan’s voters cast out the Liberal Democratic Party for only the second time in postwar history, handing a landslide victory to the opposition in hard-fought elections on Sunday. The victor, the main opposition Democratic Party, must now tackle Japan’s worsening economic problems. Almost as crucially, it faces questions here about its ability to manage the relationship with Washington. Voters set aside doubts about the untested Democrats, a broad coalition of former socialists and ruling party defectors who campaigned with promises to ease Japan’s growing social inequalities and change the way the country is governed. Continua…