How to expand cos³θ in Legendre polynomials for Griffiths 3.18

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[SOLVED] GRIFFITH 3.18 Please explain how they got this

Homework Statement


The potential at the surface of a sphere (radius R) is given by Vo=kcos3[tex]\theta[/tex]\where k is a constant. find the potential inside and outside the sphere.


Homework Equations


Their first step was:
Vo([tex]\theta[/tex]) = k[4cos^3[tex]\theta[/tex] - 3cos[tex]\theta[/tex] ]


how did they get this?

The Attempt at a Solution

 
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