Solve the following trigonometric equation: `tan3theta=-1`

Explanation

To solve the trigonometric equation \( \tan(3\theta) = -1 \), we can follow these steps:

### Step 1: Identify the angle for which the tangent is -1
We know that the tangent function is negative in the second and fourth quadrants. The specific angle where \( \tan(x) = -1 \) is \( x = -\frac{\pi}{4} + n\pi \) for any integer \( n \).

### Step 2: Set up the equation
Since we have \( \tan(3\theta) = -1 \), we can write:
\[
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