KöMaL 2017 B4853

Let $K$ denote the centre of the incircle of a circumscribed quadrilateral $ABCD$. $M$ is a point on the line segment $AK$, and $N$ is a point on the line segment $CK$, such that $2 MBN\sphericalangle= ABC\sphericalangle$. Prove that $2 MDN\sphericalangle=ADC\sphericalangle$.