12. For a regular tetrahedron \(ABCD\), construct its circumscribed sphere, where \(OC_1\) is the diameter of the sphere. Then the angle between the line \(AC_1\) and the plane \(BCD\) is \(\qquad\).
12. $\arctan \frac{\sqrt{2}}{2}$.

Construct the diameters $B B_{1}, A A_{1}, D D_{1}$, then $A D_{1} C B_{1}-C_{1} B A_{1} D$ forms a cube. The angle formed by the line $A C_{1}$ with the plane $B C D$ is the same as the angle formed by $A_{1} C$ with the plane $B C D$.