Hardy-Weinberg applied to three alleles and stimation of allele frequencies
Everybody said it already, but there is none.  The original HWE equation ($(p+q)^2=1$) works because you've got two variables and two equations ($p+q=1$) to work with (in reality, these are just one equation and one variable, since $q=1-p$ so $p+(1-p))^2=1$).  Now you have three variables and still only the one equation ($p+q+r=1$) which is, mathematically, impossible.

You need go out and measure some frequencies.  In particular, you need to measure two of them - I'd choose two of the homozygous types for convenience's sake.

This basically summarizes everything nicely for ya: http://www.bio.miami.edu/dana/dox/trinomial.html