Trigonometry of Trapeziums!

Geometry Level 5

\[\large{ \left \lfloor \left( 3 + \tan^2(x) \right) \left(\dfrac{\tan(y)}{\tan(x)} \right) + \left( \dfrac{2\sin(x) + \sin(3x)}{2\cos(x) + \cos(3x)} \right) \left( \cot(z) \right) \right \rfloor = \ ?}\]

Let \(ABCD\) be a trapezium with \(AB \parallel CD\) for which \(AD=CD\) and \(AC=BC\) and let \(E\) be the intersection of \(AC\) and \(BD\). Let \(x,y,z\) denote the measure of the angles of \(ABC, BDC, AED\) respectively. If \(y \leq 30^\circ \), find the value of the expression above.

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