I would like to understand how a Coplitts oscillator works. This link says that the tank circuit of Coplitts oscillator produces 180 degrees phase shift. I Can't understand how a combination of a coil and two capacitors produce 180 degrees phase shift. Would you explain it, please?
You must discriminate between Colpitt oscillators in common base or common emitter configuration, respectively. And - most important - you must realize that the LC tank contains a capacitive divider circuit.
The mid point between the two capacitors is either grounded (common base) or is connected to the base node (common emitter). In the first case (common base without signal inversion) the LC tank - indeed - produces 360 deg phase shift and this signal is fed back to the emitter.
In the second case (common emitter with signal inversion) the frequency dependent circuitry could be seen as a third order lowpass that consists of an first order RC lowpass followed by an LC lowpass. Such a third-order lowpass produces 180 deg phase shift at the desired frequency. The remaining 180 deg are produced by the inverting characteristic of the common emitter amplifier (between base and collector).
(Comment: The first RC lowpass function is produced with the help of the finite output resistance at the collector node. For opamp realizations (zero output resistance) you must, therefore, add a an additional resistor. Sometimes, This resistor is forgotten in in some papers).