On an inclined plane two particles `A and B` are projected with same speed at the same angle with the horizontal, particle `A` down and particle `B` up the plane. If the ratio of time of flight of `A and B` is `cot theta`, where `theta` is the angle at which `B` is projected measured from inclined plane, find the angle at which particles are projected.

Explanation

To solve the problem, we need to analyze the motion of two particles A and B projected on an inclined plane. Let's break down the solution step by step.

### Step 1: Understand the Problem
We have two particles, A and B, projected with the same speed at the same angle with respect to the horizontal. Particle A is projected down the incline, and particle B is projected up the incline. We need to find the angle of projection (denoted as α) given that the ratio of their times of flight is cot(θ), where θ is the angle of projection of particle B measured from the incline.

### Step 2: Define the Angles
Let:
- β be the angle of the incline.
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