Starting direction: You are facing, west.
\(\rightarrow\) First turn: You turn 45° clockwise.
\(\rightarrow\) From west, a 45° clockwise turn puts you in the northwest direction.
\(\rightarrow\) Second turn: You turn 180° clockwise.
\(\rightarrow\) From northwest, a 180° clockwise turn will bring you to the southeast direction.
\(\rightarrow\) Third turn: You turn 270° anticlockwise.
\(\rightarrow\) From southeast, a 270° anticlockwise turn will take you to the southwest direction.
Therefore, after all the turns, you are facing southwest