Interesting! But I don't understand why it would be the minimum though? Since its asking for the tension when the angle is 154, I assumed that the tension could be still in the process of changing.
Would this be similar to the related rates problems? Since the ropes have fixed length, it seems similar to the ladder problem where you have to differentiate its rate as it falls...
Please note that the system is not in equilibrium, and that tension must be solved for the instant where the angle is 154 degrees.
My attempt (correct ans is Ft = 626N)