Question 152
Consider the rectangular parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, in which $A B=a, B C=2 a, A A_{1}=3 a$. On the edges $C C_{1}$ and $A D$ the points $M$ and $N$, respectively, are taken such that $A N=C_{1} M=a$. Determine the measure of the angle between the lines $A M$ and $N B_{1}$.