Your linear regression model appears to be:
$E[Y|Gender,Treatment] = \beta_0 + \beta_1Male +\beta_2Treatment +\beta_3Male*Treatment$
For simplicity, Male = 1 means a male participant, Male = 0 is a female; Treatment = 1 is experimental, and Treatment = 0 is traditional.
In that case, you already have everything you need to know.
If you are interested in absolute values, you can get these as follows: The expected value of your outcome among women who receive the traditional treatment is equal to $\beta_0$. The expected value of your outcome among men who receive the traditional treatment is equal to $\beta_0 + \beta_1$. The expected value of your outcome among women who receive the experimental treatment is equal to $\beta_0 + \beta_2$. The expected value of your outcome among men who receive the experimental treatment is equal to $\beta_0 + \beta_1 + \beta_2 + \beta_3$.
If you are interested in relative values, you can get those by comparing any two of the above four absolute values. So, the ratio of the expected values of the outcome for men versus women, for all those who receive the traditional treatment, is $\frac{\beta_0 + \beta_1}{\beta_0}$. By comparison, the ratio of the expected values of the outcome for women versus men, for all those who receive the traditional treatment, is $\frac{\beta_0}{\beta_0+\beta_1}$.
EDIT: Based on your comments below, you seem to be interested in estimating the difference in test scores between the groups. To get the expected difference in test scores between any two groups, subtract the estimated average test score for those two groups: Δ=E(Y|X=x,Z=z)−E(Y|X=x′,Z=z′). So, for comparing men and women, when both receive traditional treatment, you use $(\beta_0+\beta_1) - (\beta_0) = \beta_1$. Therefore, $\beta_1$ can be interpreted as the expected difference in test scores between men and women, among those receiving the traditional treatment. Similarly, for experimental versus traditional, among women, you compare $(\beta_0 + \beta_2) - (\beta_0) = \beta_2$. So, again, $\beta_2$ can be interpreted as the expected difference in test scores between experimental and traditional treatment, among women.
If you use the same process, you can also get the expected difference in test scores between experimental and traditional treatment, among men: $(\beta_0 + \beta_1 + \beta_2 + \beta_3) - (\beta_0 + \beta_1) = \beta_2 + \beta_3$. Similarly, the expected difference between men and women, among those with the experimental treatment, is $(\beta_0 + \beta_1 + \beta_2 + \beta_3) - (\beta_0 + \beta_2) = \beta_1 + \beta_3$.
You could get these last two by recoding and re-running your regression equation, but there's no need to since you already have all the information you need in your current regression model.
First, consider the main effects and what significant two-way interactions mean. If drug and diet had a significant interaction it would mean that the average effect of diet differed by levels of drug... maybe at low drug levels the diet has a positive effect but at high drug levels, the diet has a negative effect. Thats a two-way interaction and thats why it doesn't make sense to interpret the main effects in the presence of an interaction (diet doesn't have an 'average' effect (main effect) at all, rather the effect depends on the the drug).
Now consider the three-way interaction of diet x drug x biofeedback. You've just uncovered a two-way interaction between drug and diet; the presence of the 3-way interaction tells you that at different levels of biofeedback, the nature of the 2-way interaction is different. So maybe diet has a positive effect at low levels of drug but a negative effect at high levels (your 2-way interaction) but what if that's only true at low levels of biofeedback? Maybe this interaction effect is only true at low levels of biofeedback, while at high levels of biofeedback there's no difference between diet effects by drug. That would produce a 3-way interaction. So, since the 2-way interaction depends on the 3rd variable, it's not appropriate to talk about it as an interpret-able 2-way interaction.
Best Answer
If you include an interaction term, then "the" effect no longer exists. Instead you have multiple effects: one for each level of the other variable with which you created the interaction. This is the very point of including interactions, so there is no way around it.