∵sin(a-π/4)=7√2/10
∴√2/2sina-√2/2cosa=7√2/10
∴sina-cosa=7/5 ①
∵,cos2a=7/25
∴cos2a=cos²a-sin²a
=(cosa-sina)(cosa+sina)
∴(cosa-sina)(cosa+sina)=7/25
∴-7/5(cosa+sina)=7/25
∴sina+cosa=-1/5 ②
由①②得 sina=3/5,cosa=-4/5
tana=sina/cosa=-3/4
tan(a+π/3)=(tana+tanπ/3)/(1-tanatanπ/3)
=(-3/4+√3)/(1+3√3/4)
=(48-25√3)/11