If `x\ costheta=y cos(theta+(2pi)/3)=z cos(theta+(4pi)/3)` , then write the value of `1/x+1/y+1/zdot`

Explanation

To solve the problem, we start with the given equations:

1. \( x \cos \theta = y \cos \left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right) \)

Let’s denote this common value as \( K \). Thus, we can write:

\[
x \cos \theta = K \quad (1)
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