Two parallel straight lines are inclined to the horizon at an angle `prop`. A particle is projected from a point mid way between them so as to graze one of the lines and strikes the other at right angle. Show that if `theta` is the angle between the direction of projection and either of lines, then `tan theta = (sqrt(2 - 1)) cot prop`.

Explanation

To solve the problem step by step, we need to analyze the motion of the particle projected between two parallel lines inclined at an angle \( \alpha \) to the horizontal. The particle grazes one line and strikes the other at a right angle. We will denote the angle between the direction of projection and either of the lines as \( \theta \).

### Step 1: Understand the Geometry of the Problem
We have two parallel lines inclined at an angle \( \alpha \). The particle is projected from a point midway between these lines. Let’s denote the lines as Line 1 and Line 2. The projection grazes Line 1 and strikes Line 2 at a right angle.

### Step 2: Define the Coordinate System
To simplify the analysis, we will use a coordinate system aligned with the inclined lines. We will define:
- The x'-axis along the direction of the inclined lines.
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