2009 Fermat Problem 22

In the diagram, two straight lines are to be drawn through O(0,0) so that the lines divide the figure OPQRST into 3 pieces of equal area. The sum of the slopes of the lines will be

\textbf{(A)}\ \frac{35}{24}\quad \textbf{(B)}\ \frac{7}{6}\quad \textbf{(C)}\ \frac{5}{4}\quad \textbf{(D)}\ \frac{4}{3}\quad \textbf{(E)}\ \frac{11}{8}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.