(*U(theta, alpha)*)
U = ((Cos[Pi #2 Cos[#1]] - Cos[Pi #2])/Sin[#1])^2 & ;

alphas = {0.5,1,1.25, 2} ;
s = PolarPlot[ 
Evaluate[U[t,#] & @alphas ]
, {t, 0, Pi}
, PlotRange -> {{-4,4}, {0, 5}}
]

Table[PolarPlot[ 
U[t, alphas[[a]]]
, {t, 0, Pi}
, PlotRange -> {{-4,4}, {0, 5}}
], {a, 4}]

peeters`lblPlot[s(*, {FontFamily -> \"xkcd\", 16}*)]

radres = NIntegrate[ 60 U[t, #1] Sin[t], {t, 0, Pi}] &/@ alphas
{alphas, radres} // TableForm