Medians And Bisectors

Geometry Level 5

In a right triangle, find the measure of angle \( \theta \) between the median and the angle bisector drawn from the vertex of the acute angle equal to \( \alpha \).

Now, if \( \tan\left(\dfrac{\alpha}{2}\right) = \dfrac{1}{\sqrt[3]{2}} \), enter \( \tan(\theta) \) as your answer.