Solve Particle-on-a-Ring Problem: Normalize & Write as Linear Combination

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evildarklord1985
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I have troubles to do this one problem dealing with particle-on-a-ring,

Suppose we have a wavefunction as,
g(phi) = cos(phi) + 2 sin(2phi)

First, normalize the function g(phi). By inspection, or otherwise, write g(phi) as a linear combination of eigenfunction of Lz. State what possible results for a measurement of Lz in this state would be, and what would be the corresponding probablities to obtain each one values.

Thanks for any helps!
 

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Per the rules of the forum, you have to show some attempted workings...

Relevant equations:

[tex]L_z = -i \hbar \partial_\phi[/tex]

Can you find the eigenfunctions?