import math


def luv_to_hcl(ell: float, u: float, v: float) -> tuple[float, float, float]:
    """Convert the color from CIELUV coordinates to HCL coordinates."""
    h = math.atan2(v, u)
    c = math.hypot(v, u)
    h = h + math.tau if h < 0 else h
    return h, c, ell