Let $$\theta_1, \theta_2, ......., \theta_{10}$$ be positive valued angles (in radian) such that $$\theta_1 + \theta_2 + ..... + \theta_{10} = 2 \pi$$. Define the complex numbers $$Z_1 = e^{i \theta_1}, Z_k = Z_{k - 1}e^{i \theta_k}$$ for $$k = 2, 3, ...., 10,$$ where $$i = \sqrt{-1}$$. Consider the statements P and Q given below:
$$P : \mid Z_2 - Z_1 \mid + \mid Z_3 - Z_2 \mid + .... + \mid Z_{10} - Z_9 \mid + \mid Z_1 - Z_{10} \mid \leq 2 \pi$$
$$Q : \mid Z_2^2 - Z_1^2 \mid + \mid Z_3^2 - Z_2^2 \mid + .... + \mid Z_{10}^2 - Z_9^2 \mid + \mid Z_1^2 - Z_{10}^2 \mid \leq 4 \pi$$
Then