since we know that ratio of AB : AC is 1 : √2, then we can more or less use those values for the sides, check the picture below.
so we're really looking for tan(2A). Let's bear in mind that tan²(θ) is just another way to write [ tan(θ) ]².
[tex]\bf \stackrel{\textit{Double Angle Identities}}{tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}}\\\\
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tan(2A)=\cfrac{2tan(A)}{1-tan^2(A)}\implies \cfrac{2\left( \sqrt{2} \right)}{1-(\sqrt{2})^2}\implies \cfrac{2\sqrt{2}}{1-2}\implies -2\sqrt{2}[/tex]
