Break an independent variable into two and collinearity? How to interpret the result I am not sure if the title makes sense. Here is my situation. 
I am running a regression as below:
$$ y = \alpha_0 + \alpha_1 T_1 + \alpha_2 Z + \epsilon $$
Where $T_1$ is my interested covariate: a binary variable of whether the company listed volunteer as an activity in 2008. 
I am interested to see if introducing volunteer since 2002 to 2008 will affect the outcome $y$. 
I want to break $T_1$ into two variables (and I have the data):
$T_2$: whether the company has introduced volunteer activity since 2002 to 2008, and 
$T_3$: whether the company had volunteer at the beginning. 
So basically $T_2 + T_3 = T_1$. So I am worried that $T_2$, $T_3$ and $T_1$ are correlated each other (but when I run correlation test, the correlation coefficient is very small at about $-0.1$)
What happen if I do that? Does this cause collinearity? Can you please tell me if any of these regressions will have problem? 
$$ y = \alpha_0 + \beta_1 T_2 + \beta_2 T_3 + \alpha_2 Z + \epsilon \ \ \ \ \ \ \ \ (1)$$
$$ y = \alpha_0 + \beta_1 T_2 + \alpha_1 T_1 + \alpha_2 Z + \epsilon \ \ \ \ \ \ \ \ (2)$$
Thank you!!
Edited: As suggested by @EdM I posted my regressions after the answer. 
I use Stata 13. numbacty is my outcome of interest and I use nbreg (negative binomial regression) as my estimator.
Which one is better? And can someone please give me some interpretation?
The picture below is my Equation 1. 
initialhiv is $T_3$, that is, having volunteer from the beginning.
introhivservice is $T_2$, that is, having introduced volunteer since 2002 to 2008

The picture below is the regression after using 3-level categorical factor. 
Here levelactyhiv takes the values of 0, 1, 2 if the company has no volunteer, has volunteer from the beginning and having introduced volunteer since 2002 to 2008. 

 A: It seems that you have 2 well-defined hypotheses to test: whether any "volunteer" is different from no "volunteer", and whether "volunteer" from the beginning differs from "volunteer" added from 2002 to 2008.
This might be done by recoding your $T$ variable into a single 3-level categorical factor: "no volunteer", "volunteer from the beginning", and "volunteer added from 2002 to 2008". As I understand your situation, then each case would fit into exactly one category. It doesn't really matter which you treat as the reference factor; just be careful that your analysis doesn't treat this as a numeric variable, but keeps it as categorical.
If this is set up in an analysis of variance context, you will have a test of whether there are any differences among the $\beta$ values for the 3 categories. If there aren't any differences then you are done. If there are differences then you use the information on the $\beta$ values and their standard errors to test the differences among them.
The danger in breaking out the analysis of the two "volunteer" cases, as in your equation (1), is that you lose information provided by the "no volunteer" cases. A combined analysis with more cases might be able to provide better estimates of residual errors and give you more power to detect true differences.
A: Your Eq.1 should not be an issue as long as this does not hold: $T_2(t)+T_3(t)\equiv const$
when this may happen? If your entire sample consists of volunteering companies, i.e. each company volunteered either between 2002-2008 or outside this period. In this case there's perfect collinearity. If your sample includes companies without volunteer, then there won;t be collinearity.
The interpretation is also easy: you're studying the impact of volunteering on $y$, and you're teasing out the difference between volunteering in 2002-2008 period and otherwise.
Eq.2 is slightly "worse", because the correlation between your exogenous variables is stronger due to $T_1=T_2+T_3$. However, in terms of collinearity, it's the same non-issue. Interpretation would be less clear compared to Eq.1, but still can be done.
