已知a,b属于(0,π/4),且3sinb=sin(2a+b),4tana/2=1-tan62a/2,求a+b的值

4tana/2=1-tan^2a/2
2tana/2/(1-tan^2a/2)=1/2=tana
sina=(1/2)/√(1+1/4)=√5/5
cosa=√(20/25)=2√5/5
sin2a=2*5*2/25=4/5
cos2a=3/5
3sinb=sin2acosb+cos2asinb
15sinb=4cosb+3sinb
12sinb=4cosb
tanb=1/3
sinb=(1/3)/√(10/9)=√10/10
cosb=√(1-1/10)=3√10/10
sin(a+b)=sinacosb+cosasinb
=3*√5*√10/50+2*√5*√10/50
=5*5√2/50=√2/2
a+b=π/4