Calculating synodic and sidereal period from opposition dates

If I have two consecutive dates of opposition for a planet, how can I use those dates to calculate the synodic and sidereal period?

The synodic period is time from one opposition to the next.
Only outer planets can reach opposition, use the equation below to find their sidereal period
1/(Sidereal period) =1/(Earth's sidereal period) - 1/(synodic period)

For Jupiter, the synodic period is 398.88 days
1/(Jupiter's sidereal period) = 1/365.25 - 1/398.88
Jupiter's sidereal period = 4,332.17 days = 11.86 years note all time in Earth days and years