2(1/2sinA+√3/2cosA)/2(√3/2sinA-1/2cosA)=tanB
(cos60sinA+sin60cosA)/(sin60sinA-cos60cosA)=tanB
sin(60+A)/cos(60+A)=tanB
tan(60+A)=tanB
60+A=B
1+cos（A+B/2）+cos（B+2A)=0
1+cos(3A/2+30)+cos(3A+60)=0
1+cos(3A/2+30)+cos(2(3A/2+30))=0
1+cos(3A/2+30)+cos²(3A/2+30)-1=0
(cos(3A/2+30)+1/2)²-1/4=0
cos(3A/2+30)+1/2=±1/2
cos(3A/2+30)=0 3A/2+30=90 A=40° 或者cos(3A/2+30)=-1 3A/2+30=180 A=100°（舍去,因为B=A+60=160°,A+B=100+160=260°>180°）
所以A=40° B=A+60=100°,C=180-A-B=40°