Talking about an exact solution, you'll derive the circuit loop gain and determine the L range for that the Barkhausen oscillation condition can be fulfilled. Deriving the exact loop gain in a hand calculation is rather complex, even with a circuit simulator it's not really easy.
A more practical approach is to estimate a useful range of LC circuit characteristic impedance √L/C related to the common emitter stage input- and output impedances.
Besides finding a reasonable L value for the given circuit, it should be also checked if the other circuit parameters haven been chosen suitably. How did you derive it?