Exact period, maximum value and solutions of an equation for a sum of a sine and a cosine with different frequencies

The function \(\mathrm{f}\) is defined by \(\mathrm{f}(x)=2\sin4x+\cos6x\) for \(x\in\mathbb{R}\).

1. Determine the exact period of \(\mathrm{f}\).[2]
2. Find the greatest value of \(\mathrm{f}(x)\).[1]
3. Solve the equation \(\mathrm{f}(x)=1\), giving every solution in the interval \(0\le x\le\pi\).[3]