Solve the following equations :
i) `tantheta=cottheta`, ii) `cos2theta=2sin^(2)theta`
iii) `tan3theta=-sqrt(3)`, iv) `sin2theta-costheta=0`
v) `sec^(2)2theta=1-tan2theta`

Explanation

Let's solve each of the equations step by step.

### i) Solve `tan(theta) = cot(theta)`

1. **Rewrite cotangent**: Recall that \( \cot(\theta) = \frac{1}{\tan(\theta)} \).
\[ \tan(\theta) = \frac{1}{\tan(\theta)} \]
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