How to calculate the phase difference between current and voltage?
Hints:


You can use the impedance of the R-L combination to find the current through the circuit due to each Fourier component.
You can then use Ohm's law to get the voltage across the resistor due to each Fourier component.
Then you can use the formula for power (derived from Parseval's theorem) as stated in your post to get the power.


One more hint:


Since the inductor, on average, consumes no power, the average power dissipated by the resistor is equal to the average power delivered by the sources in this circuit. So after you've found the circuit current, you might rather just calculate the source power than the resistor power.