If a,b,c be the unit vectors such that b is not parallal to c and a X(2bXc)=b then the angle that a makes with b and c are respectively where (X represents cross product)

We need to look at only one relation

Taking dot product both sides wrt a the LHS will become zero (obviously)
hence

also now we can expand the given vector triple product as

as a.b=0 and equating to RHS
Thus we get

Thus angle between a and b is 90 and angle between a and c is 60