Using tauc's relation it will help you and you can look in the theoretical derivation to determine the accuracy you can get

From the phonon spectrum it will be very difficult to calculate the indirect bandgap. However, considering an UV-Visible absorption spectra result (http://www.appropedia.org/Tauc_Plot_-_Determining_Optical_Band_Gap), you can use the Tauc plot to obtain the energy of the responsible phonon mode, as shown in the figure below, and check if this mode is possible to occur, by looking at the available phonon spectrum. Considering this, you will find out what you're looking for.

Dear Horacio Alves,

Is it possible to calculate the phonon momentum using this Tauc plot?

Dear Horacio Alves,

Can you help me to find out correct one. this tauc plot is for the band gap energy of TiO2. here modified one means bringing the actual one nearer to the X-axis but no modification nearer to Y axis.

Dear Sampath,

Based on the recent theoretical GW results of Kang and Hybertsen, Phys. Rev. B82, 085203 (2010), you are dealing with rutile structure. Their results show an indirect bandgap of 3.34 eV, which is close to the value depicted in your figure, while the value for the indirect gap of the anatase one is 3.56 eV. In order to find which phonon is responsible, I suspect that the higher LO modes should be responsible. However, it is difficult from your figure, which will be its value once we do not have a scale in the energy axis. But I can give you a hint: From the Shajee et al. paper, J. Phys. Cond. Matter 22, 015401 (2010), you will have or a A2u(LO) at 95.3 meV, or a Eu(TO) at 100.7 meV. For the anatase structure we have 93.6 and 108.6 meV, respectively. In order to analyze your data to get these values, you are doing correctly but you can let the modified curve to touch the zero values of absorption. Don't forget that integer multiples of these phonon modes can also play this role. Speculating about which energy your modified curve touch the zero value(~ 2.6 eV), we could have ~ 6 Eu(LO) modes involved.