I need to find the exact value. I'm pretty lost.

I'm assuming this means arcsec(-sqrt(2))?

So this is essentially asking "What angle has a secant of -sqrt(2)?". If it has a secant of -sqrt(2), then (since secant = 1/cosine) it has a cosine of -1/sqrt(2), which is equal to -sqrt(2)/2.

So what angle has a cosine of -sqrt(2)/2? I'm guessing you know the answer.