What i think is when we open the brackets and simplify we get

318 + 2 sin ( a+b) -80 sin b -32 cos a -150 cosb -60 sin a

Only one expression is being added i.e., sin (a+b) so to make it zero we get a + b = 0 that gives a = -b

now the expression becomes 318 - 20 sinb - 182 cosb

Now if we suppose b to be 0 we get the value as 318 - 182 that i think should be the minimum value