Answer
See explanation.
Work Step by Step
The path difference between the 2 beams cannot ever be larger than the slit spacing, d. If the distance $d=\frac{\lambda}{2}$, or is even smaller, then the 2 waves can never cancel and there will be no dark fringe.
Mathematically, the sine function is always less than 1, so if $d\leq \frac{\lambda}{2}$, there is no solution for $\theta$ in equation 35.5.
