# How do you do?

Geometry Level 5

Let $$\theta _{1}$$, $$\theta_{2}$$ and $$\theta_{3}$$ be three distinct solutions to the equation $$\tan{\theta} = \dfrac{17}{100}$$ such that $$\theta _{i} \in \left( 0 , 3\pi \right)$$, for all $$i={1,2,3}$$. Find the value of

$\tan{\dfrac{\theta_{1}}{3}} \times \tan{\dfrac{\theta_{2}}{3}} + \tan{\dfrac{\theta_{2}}{3}} \times \tan{\dfrac{\theta_{3}}{3}} + \tan{\dfrac{\theta_{3}}{3}} \times \tan{\dfrac{\theta_{1}}{3}}$

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