18.7 Let $K$ be the incenter of $\triangle ABC$, and let points $C_{1}$ and $B_{1}$ be the midpoints of sides $AB$ and $AC$, respectively. The line $AC$ intersects $C_{1}K$ at point $B_{2}$, and the line $AB$ intersects $B_{1}K$ at point $C_{2}$. If the area of $\triangle AB_{2}C_{2}$ is equal to the area of $\triangle ABC$, find the size of $\angle CAB$.