x+y=π/4,
tanx+tany=1-tanxtany,
(1+tanx)(1+tany)
=1+(tanx+tany)+tanxtany
=2.
积化和差公式
sin(π/4+x）*sin(π/4-x）
=－1/2[cos π/2-cos2x]
=1/6.
cos2x=1/3>0,
又x∈（－2π,π）,