Answer
The minimum tension is 5.89m, and this tension occurs at 40 degrees.
Work Step by Step
The problem asks us to plot $\frac{T}{mg}$ versus the value of theta. Thus, we plot the following function:
$\frac{T}{mg}=\frac{\mu_k}{cos\theta+\mu_ksin\theta}=\frac{.75}{cos\theta+.75sin\theta}$
The shape of this is roughly parabolic, and the minimum of the graph is about .60, and this occurs at around 40 degrees. Thus, the minimum tension is 5.89m, and this tension occurs at 40 degrees.
