Answer
£=-4
Work Step by Step
As the maximum force is 2F` when theta is equal to 180° ( B is left of A, while C is right of A ).
So, we choose the minus sign and write
2F`= ( 1-1÷4£)F`
£= -4
On the way to think minus sign choice is cos (180°) = -1. This is certainly consistent with the minimum force ratio ( zero ) at theta is equal to 0° since that would also imply
0= 1+1÷4£
£=-4
