BLUE of $\beta_2$ from three uncorrelated, homoscedastic linear combinations

Consider the model $E(Y_1)=\beta_1+\beta_2, E(Y_2)=\beta_1-\beta_2,\ E(Y_3)=\beta_1+2\beta_2$ with the assumption that $Y_i$'s are uncorrelated and $\var(Y_i)=\sigma^2$ for all $i=1,2,3$. Then the best linear unbiased estimator of $\beta_2$ is: