Two vectors $$\hat{A} and \hat{B}$$ are defined as $$\hat{A}$$=a $$\hat{i}$$ and $$\overrightarrow{B}=a(\cos \omega t \hat{i}+\sin \omega t \hat{j})$$, where a is a constant and $$\omega=\frac{\pi}{6} rad s^{-1}$$.If $$\mid \overrightarrow{A}+\overrightarrow{B}\mid$$=$$\sqrt{3} \overrightarrow{A}-\overrightarrow{B}$$ at time t = $$\tau$$ for the first time,
the value of $$\tau$$, in Seconds, is .................