$I_{A2}=\frac{U}{R}$

$I_{A1}=\frac{U}{\frac{2}{3}R}$

$I_{A1}=\frac{3U}{2R}$

$I_{A1}=\frac{U}{R_{z1}}$

$R_{12}=R_1+R_2$

$R_{12}=2R$

$\frac{1}{R_{z1}}=\frac{1}{R_{12}}+\frac{1}{R_3}$

$\frac{1}{R_{z1}}=\frac{1}{2R}+\frac{1}{R}$

$\frac{1}{R_{z1}}=\frac{3}{2R}$

$R_{z1}=\frac{2}{3}R$