If equation `|sqrt((x-tantheta)^(2)+(y-sqrt3tantheta)^(2))-sqrt((x-2tantheta)^(2)+y^(2))|=2,theta in[0,pi]-{(pi)/(2)}` represents hyperbola, then find the value of `theta`.

Explanation

To solve the problem step by step, we start with the given equation:

\[ |\sqrt{(x - \tan \theta)^2 + (y - \sqrt{3} \tan \theta)^2} - \sqrt{(x - 2 \tan \theta)^2 + y^2}| = 2 \]

### Step 1: Understand the Equation
The equation represents the absolute difference between the distances from a point \( P(x, y) \) to two fixed points \( F_1(\tan \theta, \sqrt{3} \tan \theta) \) and \( F_2(2 \tan \theta, 0) \).
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