Let the line x+y=1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the…

Let the line $\displaystyle x+y=1$ meet the axes of $\displaystyle x$ and $\displaystyle y$ at A and B , respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB , respectively. If the area of the triangle AMN is $\displaystyle \frac{4}{9}$ of the area of the triangle OAB and $\displaystyle \mathrm{AN}: \mathrm{NB}=\lambda: 1$, then the sum of all possible value(s) of is $\displaystyle \lambda$ :