Let $W=\{W_t: t \geq 0\} $ be the standard Brownian motion.
The quadratic variation for a stochastic process $X=\{X_t: t \geq 0\}$ is defined has $$[X,X]_t=\lim_{n\to \infty}\sum_{i=1}^n (X_{t_i}-X_{t_{i-1}})^2=\int_0^t(dX_s)^2$$ where $t_i=\frac{ti}{n}$ and the limit is in $L^2$ sense.
How can I compute $[|W|,|W|]_t$ , i.e. the quadratic variation of $|W_t|$?
(I've tried using Tanaka's formula but I think the exercise wanted me to do it differently)