= Solution
The <Weiss zone law> gives $u+w=0$ and $u-v=0$, so a common direction is \b[$[11\bar1]$]. Its physical vector is $(a,a,-c)$, while $[100]$ is parallel to $(a,0,0)$. Their <dot product> therefore gives
$$
\boxed{\theta=\cos^{-1}\!\frac{a}{\sqrt{2a^2+c^2}}=49.80^\circ}.
$$
Taking a Euclidean angle directly between the index triples would incorrectly treat the tetragonal axes as equal in length. Reversing the chosen common direction gives the supplementary oriented angle.
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