Let a and b be two non-zero vectors perpendicular to each other and | a |=| b |. If | a × b |=| a |, then the angle between the vectors ( a + b +( a…

Let $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}$ be two non-zero vectors perpendicular to each other and $\displaystyle |\overrightarrow{\mathrm{a}}|=|\overrightarrow{\mathrm{b}}|$. If $\displaystyle |\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}|$, then the angle between the vectors $\displaystyle (\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}))$ and $\displaystyle \overrightarrow{\mathrm{a}}$ is equal to: