sin(A+π/4)=sinA·cosπ/4+cosA·sinπ/4
=√2/2(sinA+cosA)=1/3
sinA+cosA=√2/3→cosA=√2/3-sinA带入下式
(sinA)^2+(cosA)^2=1
解得：sinA=（√2+4）/6 或 sinA=（√2-4）/6（舍去）←A∈（π/2,π)
因此sinA=（√2+4）/6