Harbour tide level from consecutive low tides

A harbour is at low tide of \(1.2\) metres at 1 pm on \(10^{\mathrm{th}}\) June 2025, and it next reaches a low tide at 11 pm on that day.

The tide level in the harbour, \(H\) metres, at a time \(t\) hours from noon on \(10^{\mathrm{th}}\) June 2025, can be modelled by the equation \(H(t)=a\cos\bigl(b(t-c)\bigr)+1.5\), where \(a\), \(b\) and \(c\) are real, positive constants and \(t\in\mathbb{R}\).

1. Find the value of \(a\) and the value of \(b\).[4]
2. State the smallest possible value of \(c\).[1]
3. Using your answers to parts (a) and (b), find the first possible time at which a tide level of \(1.65\) metres is recorded on \(11^{\mathrm{th}}\) June 2025.[4]