Find $\arctan x_1 \cdot \arctan x_2$, where $x_1$ and $x_2$ are roots of $x^2 - 2\sqrt{2}x + 1 = 0$. I am told that $x_1$ and $x_2$ are the roots of the following equation:
$$ x^2 - 2\sqrt{2}x + 1 = 0 $$
And I have to find the following:
$$\hspace{6cm} \arctan x_1 + \arctan x_2 \hspace{5cm} (1)$$
$$\hspace{6.cm} \arctan x_1 \cdot \arctan x_2 \hspace{5.3cm} (2)$$
Now I know that, in general:
$$\arctan(a) + \arctan(b) = \arctan \bigg ( \dfrac{a + b}{1 - ab} \bigg )$$
So $(1)$ is not that difficult to find, it actually equals $\dfrac{\pi}{2}$. 
The problem is that I don't know how to find $(2)$.

The roots of the equation are $ x_1 = \sqrt{2} + 1$ and $ x_2 =\sqrt{2} - 1 $. So we can explicitly work out $ \arctan(x_1) \, \cdot \, \arctan(x_2) = \frac{\pi}{8} \, \cdot \, \frac{3\pi}{8} = \frac{3\pi^2}{64} $
