To know the exact value of tan(157.5°), you only have to enter the value in your calculator:
First, press the buttton identified as "tan" and then write 157.5. The next step you must follow is press the button with the symbol of equal: "="
Now, the value of tan(157.5°) will appear on the screen of you calculator.
As you can see, the exact value of tan(157.5°) is:
tan(157.5°)=-0.4142