= Solution
Let $\ell=\ln(\theta_{\max}/\theta_{\min})$. The supplied second moment gives the single-scatter <root mean square> angle
$$
\theta_{\rm rms,1}=\sqrt{\langle\theta^2\rangle}\simeq\sqrt2\,\theta_{\min}\sqrt\ell.
$$
For independent scatters with uniform azimuth, the small angular-deflection vectors have zero mean. Their cross terms average to zero, so their <variances> add. After $N$ scatters,
$$
\boxed{\operatorname{RMS}(\theta)=\sqrt{N\langle\theta^2\rangle}
\simeq\theta_{\min}\sqrt{2N\ell}.}
$$
This is the <root mean square> magnitude of the two-dimensional angular deflection. Its projection into one specified plane has a <variance> smaller by a factor of two, hence a <root mean square> smaller by $\sqrt2$.
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