FIND

sin ( a+b) =1 => a+b= 90^o  and sin(a-b) =1/2  => a-b = 30^o

this is possible only if 0a,b90^o  since  0a+b180^o and -90^oa-b90^o

so a= 60^o and b = 30^o

tan(a+2b) = tan(120^o ) = -3^1/2

tan (2a+b) = tan(150^o ) = -1/ 3^1/2