how to calculate the exact frequency of this FM transmitter?

Nice thought, but you really don't want a stable frequency for wideband FM, you
have to shift the frequency +/-200kHz or so according to the modulation input,
0.1% or so, far more than a crystal can be "bent". Narrowband FM can be done
with crystals (deviation is more like 2.5kHz), wideband you need either PLL or DDS
techniques or an modulated LC oscillator like this.

The frequency is set by the tank circuit, C6/L1, since C6 is a trimmer anyway that
should give a wide range of adjustment.

Without a spectrum analyser you'll have to use a radio receiver to tune this
transmitter.

Note that this circuit is primitive and the antenna will affect the tuning so you must
tune with the antenna you will be using.