Estimability with four linked expectations — identify the one genuinely non-estimable combination

$y_1,y_2,y_3,y_4$ are four uncorrelated random variables with common variance $\sigma^2$ and $E(y_1)=E(y_2)=\theta_1+2\theta_2+\theta_3,\ E(y_3)=E(y_4)=\theta_1+\theta_3$. Hence: