sin(3r)=sin(2r+r)=sin(2r)cos(r)+cos(2r)sin(r)=2sin(r)cos²(r)+(2cos²-1)sin(r)=2sin(r)(1-sin²(r))+(1-2sin²(r))sin(r)=3sin(r)-4sin³(r)
令r=a/3得sin(a)=3sin(a/3)-4sin³(a/3).........①
划为sin³(a/3)-3/4sin(a/3)+1/4sin(a)=0
Δ=(1/4sin(a))²+(1/4)³=1/16sin²(a)+1/64
有一实根和两复根
sin(a/3)=³√(-1/8+²√(1/16sin²(a)+1/64) ) +³√(-1/8-²√(1/16sin²(a)+1/64) ).............② 后略。楼主考虑①即可