Identifying a LC oscillator circuit and solving resonance frequency
Here's a generic AC model* of a Colpitts oscillator that matches yours**.  The tank circuit is formed by the series combination of C3 and C4, in parallel with Cextra and L1.  In your case, Cextra is the series combination of C5 and the diode capacitance (which varies with voltage).  C6 and the following stage complicates things -- that stage's input impedance is probably high enough to not matter, but if it's between about \$300\Omega\$ and \$50\Omega\$ then it could pull the frequency down (and reduce the Q of the oscillator).

So, calculate the overall capacitance, then calculate the resonant frequency given L1 (which you don't know), and that's your tank circuit's resonant frequency.  Hopefully the oscillator is designed well enough that the oscillator runs close to the tank circuit's resonant frequency.

* "AC model" meaning that I'm ignoring the bias networks.

** I left it ungrounded on purpose -- you can ground any point on that circuit and it's still a Colpitts; the only thing that changes is where you pick off the output signal, and how hard it is to bias.







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