sin(a+π/4)sin(a-π/4)=(sinacosπ/4+cosasinπ/4)(sinacosπ/4cosasinπ/4)=[√2/2(sina+cosa)][√2/2(sina-cosa)]=1/2(sin²a-cos²a)=1/3sin²a-cos²a=2/3cos2a=cos²a-sin²a=-2/3cos4a=2cos²2a-1 =2×(-2/3)²-1 =-1/9
