Solution:

Because the angle is acute.

So ya = √ [1-(√ 2/10) 2] = 7 √ 2/10.

yB=√[ 1-(2√5/5)^2]=√5/5

Therefore, tana = ya/xa = (7 √ 2/10)/(√ 2/10) = 7.

tanb=yB/xB= 1/2

tan(a+b)=(tana+tanb)/( 1-tana tanb)=( 1/2+7)/( 1-7/2)=-3

tan(a+2b)= tan(a+b+b)=[tan(a+b)+tanb]/( 1-tan(a+b)tanb)

= (-3+1/2)/(1-3) * (1/2)) =-1.Because both A and B are acute angles, a+2b=3π/4.

Note: A is angle α, and B is angle β.