This is a basic level question as I have no prior experience with optimizing on shapes. I have a dataset and I am fitting a model to it. The equation of the model I want to fit is
$$R(0,\theta)=\beta_0+\beta_1 \left[ \frac{1-\exp(-\frac{\theta}{\tau_1})}{\frac{\theta}{\tau_1}} \right] + \beta_2 \left[ \frac{1-\exp(-\frac{\theta}{\tau_1})}{\frac{\theta}{\tau_1}} - \exp \left(-\frac{\theta}{\tau_1} \right) \right] + \beta_3 \left[ \frac{1-\exp(-\frac{\theta}{\tau_2})}{\frac{\theta}{\tau_2}} - \exp \left(-\frac{\theta}{\tau_2} \right) \right].$$
Here I have to model $R$ with $\theta$.
Now I want to optimize this data such that the shape of my $\theta$~$R$ graph is of almost fixed shape Something like this.
I have no idea how to proceed with this, so any help would be appreciated.