If

\(\cos^2\theta = \dfrac{m^2 -1}{2} and \tan^3\dfrac{\theta}{2} = \tan\alpha\)

and on simplification and elimination of \(\theta\), we get an equation of the form,

\(\displaystyle a\cos^{\frac{2}{3}}\alpha + b\sin^{\frac{2}{3}}\alpha = \dfrac{c^{\frac{2}{3}}}{(dm)^{\frac{2}{3}}}\)

Find \(a+b+c+d\)

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