A geometry problem by Aakhyat Singh

Geometry Level 3

If $$x\cos A=y \cos \left(A+\dfrac {2\pi}3\right) = z \cos \left(A+\dfrac {4\pi}3\right)$$, then find the value of $$\dfrac 1x+\dfrac 1y + \dfrac 1z$$.

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