Calculate the time it takes for the reoccurence of opposition between Earth and Mars

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Homework Statement


9lkj6v.jpg


Homework Equations


From Wikipedia:
43908428570eafb92e2cbf616b587a4b.png

E = the sidereal period of Earth (a sidereal year, not the same as a tropical year)
P = the sidereal period of the other planet
S = the synodic period of the other planet (as seen from Earth)

The Attempt at a Solution


This problem requires me to actually "think" / make out / derive such an equation to calculate the time it takes for another opposition planetary alignment to re-occur between Earth and Mars. The problem, as shown in the diagram, gives me pure facts and I simply have no idea of how to start. For example, I do not know what are the important variables I must incorporate to compose such equation and I don't know how to mathematically relate the circular motion of Mars and Earth.

I have found an article on wikipedia showing me the way to calculate this so called synodic period which I believe is what I am looking for.

But, wikipedia doesn't tell me how exactly this equation is derived and I really want to learn the derivation. So anyone, please guide me.
 

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