Where does the helix r(t) = kcos t, sin t, t) intersect the paraboloid z = x

Where does the helix r(t) = kcos πt, sin πt, t) intersect the paraboloid z = x² + y²? What is the angle of intersection between the helix and the paraboloid? (This is the angle between the tangent vector to the curve and the tangent plane to the paraboloid.)