= Solution
At leading order in $|k\tau|$, the inflationary <Fourier mode> and its derivative are
$$
f_k\simeq-\frac{i}{\sqrt{2k^3}\tau},
\qquad
f_k'\simeq\frac{i}{\sqrt{2k^3}\tau^2}.
$$
Thus the leading parts of $\hat f$ and $\hat\pi$ contain the same quadrature of the <creation and annihilation operators> and satisfy
$$
\hat\pi\simeq-\frac1\tau\hat f.
$$
Their commutator consequently vanishes in this leading approximation. The exact nonzero result in part b is carried by the subleading decaying mode. Relative to the rapidly growing anticommutator, its effect is suppressed by powers of $|k\tau|$, which is the squeezing captured by the <classicality parameter of a cosmological perturbation>. The perturbation can therefore be treated as an effectively classical stochastic field on <superhorizon scales> even though its exact quantum commutator is unchanged.
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