Answer
$F$ would be maximum when $\theta=0^\circ$
Work Step by Step
From part b), we get an approximation formula of $F$:
$$F\approx2.9W\cos\theta$$
In this exercise, consider that $W$ is unchanged and the only variable is $\theta$, we need to find at which value of $\theta$ that $F$ is maximum.
Here, since $2.9W$ is unchanged, $F$ is maximum when $\cos\theta$ is maximum.
We already know the range of $\cos\theta$ is $[-1,1]$. In other words,
$$-1\le\cos\theta\le1$$
Therefore, the maximum value of $\cos\theta$ is $1$, occurring when $\theta=k180^\circ$ $(k\in Z)$.
However, in this exercise we only consider the capacity of a straight back making an angle of $\theta$ with the horizontal, so $0\le\theta\le180^\circ$.
So the maximum value of $\cos\theta$ is $1$ occurring when $\theta=0^\circ$.
That means, overall, $F$ would be maximum when $\theta=0^\circ$