= Solution
For $0<\mu<1$, all orbits converge to one fixed point, and for $\mu=1$ every orbit is eventually fixed or period two, so no iterate has a horseshoe. For the symmetric <tent map> with slope magnitude $\mu>1$, the <topological entropy> is $\log\mu>0$. The <interval-map positive-entropy horseshoe theorem> says that a continuous <interval map> has <positive topological entropy> exactly when some <iteration of a map>[iterate] has a <horseshoe for an interval map>[horseshoe]. Hence
$$
\boxed{F\text{ is chaotic in Glendinning's sense exactly when }1<\mu\leq2}.
$$
For $\mu\geq\sqrt2$ this already follows from part (iii); for $1<\mu<\sqrt2$, a higher iterate supplies the horseshoe.
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