No, when we are sure that there are two close peaks. What I would do is to fit the observed signal to the sum of two lorentzian peaks plus an offset (or linearly varying background). The fitted parameters would be positions, amplitudes and FWHM's plus non-interesting background parameter(s), together with their uncertainties. By the way: how did you get so precise value of 2\theta? That's incredible.
I analysised my powder with XRD and then I want use than the Origin software and calculate amount grain size with Sherrer formula , I have to use than FWHM for some peaks to have precise value , in its spectra there are two peaks very big and there are very close together ...
With Origin you can calculate FWHM, I suggest to have a look on following references for your both questions (In the Sherrer formula for calculation grain size , How must I choose the K constant for my work?):
1) Precursor and Reaction Time Effects in Evaluation of Photocatalytic Properties of TiO2 Nanoparticles Synthesized via Low Temperature
Int. J. Electrochem. Sci 9, 3068-3077
2) Influence of temperature and surfactant on the photocatalytic performance of TiO2 Nanoparticles
At the mentioned angle, You have two overlapping diffraction lines, Therefore you can use one of two methods. The first method is the graphical method, in which you will draw the two peaks and manually completing them. noting that you must smooth them, then measuring the height of each peak and then find FWHM of each.
The second one is a via a computer program to make deconvolution of the two peaks,