2021 DHS P1 Q2

A triangle $ABC$ is such that $AC=\sqrt{2}$, $BC=4$ and angle $ACB=\frac{1}{4}\pi +\theta $. Given that $\theta $ is sufficiently small for ${{\theta }^{3}}$ and higher powers of $\theta $ to be neglected, show that

$AB\approx \sqrt{10}\left[ 1+a\theta +b{{\theta }^{2}} \right]$,

where $a$ and $b$ are real constants.

[5]