Given the cube $(ABCD,A_{1}B_{1}C_{1}D_{1})$ with $D(0,0,0),A(5,0,0),B(5,5,0),C(0,5,0),C_{1}(0,5,5),K(5,5,4)$ and so on.
Line, through $K$ and $//BD_{1}$, cuts $DD_{1}$ in the point $I$.
The line $IC_{1}$ cuts $DC$ in the point $J$.
The line $IK$ cuts $DB$ in the point $L$; plane $a \cap (ABCD) = JL$.
$JL$ cuts $DA$ in the point $M$ (not to see in the drawing).
$MI$ cuts $AA_{1}$ in the point $N$.
$NK$ cuts $A_{1}B_{1}$ in the point $O$; plane $a = (C_{1}KO$.
$OC_{1}$ cuts $IK$ in the point $P(4,4,5)$.
Equation of the plane $a\ :\ x+4y+5z=45$.
$\cos \alpha=\frac{4}{\sqrt{42}}$.
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