# Chocolate mania (mechanics +trigonometry)

Classical Mechanics Level 4

Cody is this time throwing a chocolate from the ground and the $$\color{Red}{\text{lady}}$$ is on the top of the building to catch it.

The point from where Cody throws the chocolate is $$180\, \text{m}$$ away from the building and building is $$360\,\text{m}$$ tall.

Given that when the $$\color{Red}{\text{lady}}$$ caught the chocolate, it was travelling horizontally (vertical velocity $$0\,\text{m/s}$$) and Cody had thrown the chocolate with the initial velocity making an angle $$\theta$$ with the horizontal, then find the value of

$\tan \theta \times \tan (60^\circ -\theta) \times \tan(60^\circ +\theta)$

This value can be written as $$\dfrac{a}{b}$$ for coprime positive integers $$a$$ and $$b$$ . then find the value of $$a+b$$.

Details: In this problem, you don't need the initial velocity at all, neither the value of acceleration due to gravity.

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