Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle `45^0` and its slope becomes `3.` Find the angle `thetadot`

Explanation

To solve the problem step by step, we need to find the angle \( \theta \) given that a line with an initial angle \( \theta \) is rotated by \( 45^\circ \) and its slope becomes \( 3 \).

### Step 1: Define the initial slope
Let the initial slope of the line be \( m_1 = \tan(\theta) \).

**Hint**: Remember that the slope of a line is defined as the tangent of the angle it makes with the positive x-axis.

### Step 2: Define the new slope after rotation
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