原式
=cos²a+(cosπ/3cosa+sinπ/3sina)²+(cosπ/3cosa-sinπ/3sina)²
=cos²a+(1/2*cosa+√3/2sina)²+(1/2*cosa-√3/2sina)²
=cos²a+1/4*cos²a+3/4sin²a+1/4*cos²a+3/4sin²a
=cos²a+3/2sin²a
=3/2+1/2*sin²a