From sine theorem: a/sina = b/sinb = c/sibc: c = bsinc/sinb, a=bsinA/sinB,

∫3 bcosa = ccosa+acosc ∴3bcosa=bsinccosa/sinb+bsimacisc/sinb

3sinBcosA=sinCcosA+simAcosC

∫a+b+c = 180 ∴sinccosa+sinacosc=sin(a+c)=sin( 180-b)= sinb

∴ 3 sinbcosa = sinb3kossa = 1 kossa = 1/3

∵(sina)^2+(cosa)^2= 1 a < 180

∴sinA= root number [1-(COSA) 2] = root number [1-( 1/3) 2] = root number (8/9)=(2 root number 2)/3.

∴tanA=sinA/cosA=2 root number 2.