# Sink Cost Tank Cots

Geometry Level 5

$\dfrac{\sin^{2y}x}{\cos^{\frac{y^2}{2}}x} + \dfrac{\cos^{2y}x}{\sin^{\frac{y^2}{2}}x} = \dfrac{2\tan x}{1+\tan^2x}$

There are $$n$$ pairs of real numbers $$x,y$$, such that $$\ x \in \Big( 0, \dfrac{\pi}{2} \Big)$$ , that satisfy the above equation.
Let $$\alpha=\dfrac{4}{3} (x_1y_1 + x_2y_2 + \cdots + x_ny_n)$$

Then the value of$$(\sin \alpha + \sin 4\alpha + \sin 7\alpha + \cdots + \sin 298\alpha)$$ can be expressed as $$a \sqrt b$$, where $$a$$ and $$b$$ are positive integers with $$b$$ is square free. Find $$a+b$$.

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