A picture paints a thousand words (I hope). In the diagram the arrows represent forces. The length is proportional to the size of the force (is size correct? I am not a native speaker). I could bore you to death with sinus, tan and cosines to calculate the relation between the forces. Bottom line is that each stake needs to hold approximately 40% of your weight in the direction given in the diagram. That is a lot. The force on the base plate will be about 150% of your weight, but that will not be your first concern.
BTW have a look at the anchor of the treemount stand. It is supplied with 6 double stakes!