Answer: \(y=1.96\) or \(y=5.10\).

Use the standard trigonometric identities and make sure the final angles are chosen from the interval given in the question.

Since \(\cot(y+1.5)=3\),

\(\tan(y+1.5)=\frac13.\)

Let \(u=y+1.5\). Since \(0\lt y\lt 6\),

\(1.5\lt u\lt 7.5.\)

The principal value is

\(\tan^{-1}\left(\frac13\right)=0.32175\ldots.\)

In the interval \(1.5\lt u\lt 7.5\), the solutions are

\(u=0.32175\ldots+\pi\quad\text{and}\quad u=0.32175\ldots+2\pi.\)

Therefore

\(y=1.963\ldots\quad\text{or}\quad y=5.105\ldots.\)

So

\(y=1.96\quad\text{or}\quad y=5.10.\)

This gives the required answer: \(y=1.96\) or \(y=5.10\).