$\left[\begin{array}{l}\text { [Inscribed, circumscribed, and exscribed circles; their radii] } \\ {[\text { Auxiliary similar triangles }}\end{array}\right]$

In parallelogram $A B C D$, side $A D$ is equal to 6. The bisector of angle $A D C$ intersects line $A B$ at point $E$. A circle is inscribed in triangle $A D E$, touching side $A E$ at point $K$ and side $A D$ at point $T, K T=3$. Find angle $B A D$.
As can be seen from the solution to the problem $\underline{52925}$, if the distance between the points of tangency of the inscribed circle in an isosceles triangle with the lateral sides is equal to half the lateral side, then this triangle is equilateral.

## Answer

$60^{\circ}$.