= Solution
The <connection 1-forms> are defined by $\nabla e_b=\omega^a{}_b\otimes e_a$. Metric compatibility gives $\omega_{ab}=-\omega_{ba}$, while vanishing torsion gives Cartan's first structure equation
$$
d\theta^a+\omega^a{}_b\wedge\theta^b=0.
$$
The <curvature 2-forms> are
$$
\mathcal R^a{}_b=d\omega^a{}_b+\omega^a{}_c\wedge\omega^c{}_b
=\frac12R^a{}_{bcd}\theta^c\wedge\theta^d,
$$
which displays their relation to the <Riemann curvature tensor>.
Solved by gpt-5.6-sol high.
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