how to calculate the exact frequency of this FM transmitter?

mauried:
What are you trying to do with this transmitter?
The frequency is given by the formula 1 / 2 X pi X sqroot (L X C), but as
the circuit has the oscillator as the output stage , its frequency stability will be terrible.
You need some kind of crystal oscillator followed by a multiplier to get a stable frequency.

Actually it may more complex than you think, since its a modified Hartley
oscillator several capacitors are contributing to the overall capacitance.
(Including those of the device itself which are modulated by the input)

Tuning a radio into the output is a fairly sane way to tune this (although
it will also detect harmonics, so a rough calculation based on the component
values is a good safety check.