The critical temperature for Bose-Einstein condensation of a gas in a 3D harmonic trap is $T_c = \\frac{\\hbar \\omega}{k_B} \\left( \\frac{N}{\\zeta(3)} \\right)^{1/3}$. If the trap contains $N = 1.202 \\times 10^6$ atoms, the trap frequency is $\\omega = 200\\pi$ rad/s, and $\\zeta(3) \\approx 1.202$ is the Riemann zeta value, what is the critical temperature $T_c$ in microkelvins ($\\mu$K)? (Use $\\hbar = 1.054 \\times 10^{-34}$ J\cdot s and $k_B = 1.38 \\times 10^{-23}$ J/K).