π/3 或者2π/3
设抛物线为y²=2px,设点A(x1,y1)B(x2,y2)
则AP=x1+p/2,PB=x2+p/2,∴AB=x1+x2+p
交点为(p/2,0)
若直线AB不垂直X轴,设直线AB为：y=k(x-p/2),代入抛物线方程,消去y得k²x²-(pk²+2p)x+k²p²/4=0,故x1+x2=(pk²+2p)/k²=p+2p/k²
故|AB|=p+2p/k²+p=2p(1+1/k²)=2p(1+cot²a)=2pcsc²a=2p/sin²a
∴2p=|AB|sin²a ...(1)
2p=4 |AB|=16/3 得sin²a=3/4
α=π/3 或者2π/3