I2.1 In Figure $1, A B C D$ is a square, $M$ is the mid-point of $A D$ and $N$ is the mid-point of $M D$. If $\angle C B N: \angle M B A=P: 1$, find the value of $P$.
Let $\angle A B M=\theta, \angle C B M=P \theta$. Let $A B=4, A M=2, M N=1=N D$.
$$
\begin{array}{l}
\tan \theta=\frac{1}{2} \\
\tan 2 \theta=\frac{2 \tan \theta}{1-\tan ^{2} \theta}=\frac{2 \times \frac{1}{2}}{1-\left(\frac{1}{2}\right)^{2}}=\frac{4}{3}=\tan P \theta, P=2
\end{array}
$$