MathNet 2007-part-01 — 187 problems (EN–VI) Question 89

The edge $DA$ of a pyramid $ABCD$ is perpendicular to its base $ABC$, $(ABD) \perp (BCD)$, $\angle BDC = 45^\circ$ and $DB = 2$. Find $\angle ADB$ if the sum of the squares of lateral faces of the pyramid equals $8$.