Focusing on Incentres!

A triangle $ABC$ is given as of above such that $2AB = 3AC$ . The midpoints of the sides $AC$ and $AB$ are $B_1$ and $C_1$ respectively. The centre of the incircle of $\Delta ABC$ is $I$ . The lines $B_1I$ and $C_1I$ meet the sides $AC$ and $AB$ at $B_2$ and $C_2$ respectively.

Given that the areas of $\Delta ABC$ and $\Delta AB_2C_2$ are equal, find the value of $\angle BAC$ in degrees .

Note:

• Incentre is the point of concurrency of the angle bisectors of a triangle.

• Points $D$ and $E$ are mentioned specifically for clarity.