# 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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