BALTIC-WAY 2014 Problem 5

Given positive real numbers $a, b, c, d$ that satisfy equalities

$$a^{2}+d^{2}-a d=b^{2}+c^{2}+b c \text { and } a^{2}+b^{2}=c^{2}+d^{2}$$

find all possible values of the expression $\frac{a b+c d}{a d+b c}$.