Force needed to raise a backpack

[syllll_213]

Homework Statement

The question is asking how the force needed to raise the pack change, but I am unsure if my working and reasoning is right. Particularly, I am unsure if I can assume both the angles (theta) I labelled to be equivalent because I sort of assumed the force pulled by the guy to be equal to the force pulling on the backpack. Some comment on my working would be appreciated thank you TT.

Relevant Equations

F=ma

 

[haruspex]

The diagram provided seems to have misled you a little. It shows the hiker pulling down at some angle to the vertical but labels a vertical force $\vec F$.
How does the force with which the hiker pulls on the rope relate to the tension in the lateral section of the rope?

Also, you seem to have forgotten the contribution from the right half of the rope.