tan（α+π/4）+tan（α+3π/4）
=(tanα+tanπ/4)/(1-tanαtanπ/4)+(tanα+tan3π/4)/(1-tanα+tan3π/4)
=(tanα+1)/(1-tanα)+(tanα-1)/(1+tanα)
={(tanα+1)*(1+tanα)+(tanα-1)*(1-tanα)}/{(1+tanα)*(1-tanα)}
=(4tanα)/(1-tan^2α)
=2tan2α