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I'm not sure, that i correctly understood your question and that its algorithm is completely correct, but idea must work, i think

double minAbsBearing = Integer.MAX_VALUE;
double minRelBearing = Integer.MAX_VALUE;
double maxRelBearing = Integer.MIN_VALUE;

for (ATarget target : enemys) {
    double absBearing = ...; // me.angleTo(target) in my case
    double relBearing = Utils.normalRelativeAngle(absBearing);
    if (relBearing < minRelBearing) {
        minAbsBearing = absBearing;
        minRelBearing = relBearing;
    } 
    if (relBearing > maxRelBearing) {
        maxRelBearing = relBearing;
    }
}

double widestArea = maxRelBearing - minRelBearing;
double startAngle = minAbsBearing;
double endAngle = Utils.normalAbsoluteAngle(minAbsBearing + widestArea);