A flagstaff is on the top of a tower which stands on a horizontal plane.

A person observes the angles subtended by the flagstaff and the tower at a point on the horizontal plane as \(\alpha\) and \(\beta\) respectively.

He then walks a distance \(a\) towards the tower and observes that the angle subtended by the flagstaff remains unchanged.

Enter the height of the tower correct to three decimal places.

**Details and assumptions:**

- \(\alpha=15^\circ\)
- \(\beta=30^\circ\)
- \(a=2\)

**Clarification figure:**

**Bonus questions:**

- Generalise for arbitrary values of \(\alpha, \beta\) and \(a\).
- Find the height of the flagstaff in this generalised situation.

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