Answer
$\theta=60^{\circ}$
Work Step by Step
Since the normal force needs to be half of the weight for slipping to happen, it can be stated that $$N=\frac{1}{2}w$$ Since the weight equals $mg$ and $N=mgcos\theta$, the expression becomes $$\frac{1}{2}mg=mgcos\theta$$ Dividing each side by $mg$ yields $$\frac{1}{2}=cos\theta$$ The value of theta that satisfied the equation is $\theta=60^{\circ}$.
