# It's Time To Have Pi Today

Geometry Level 4

$4\left( \arctan\left( \dfrac { 1 }{ x } \right) + \arctan\left( \dfrac { 1 }{ { x }^{ 3 } } \right) \right) =\pi$

Let $$x$$ be the positive real number satisfying the equation above and $${x}^{3}-x$$ can be expressed as

$\dfrac { a }{ b } \left( c+\sqrt { d } \right) \; ,$

where $$a, b, c$$ and $$d$$ are positive integers, with $$a,b$$ coprime and $$d$$ square-free.

Find the value of the expression below.

$4\left( \arctan\left( \dfrac { b }{ c } \right) + \arctan\left( \dfrac { a }{ { d } } \right) \right)$