Hey rashmil.

You may have to use a numerical solver for this problem, but never the less you need all beta terms on one side and everything else on the other.

Hint: Use e^(a+b) = e^a * e^b and get everything in terms of Beta on LHS (You will have a cos term and an exponential term that are functions of beta).

If you need to use a numerical solver, then something like MATLAB (or Octave) should suffice. You could also R as well which is free (as is Octave).