What is the exact value of sin(cos^−1(−2√2))+tan^−1(sin(π/2))?

cos^-1( -2·sqrt(2) )  does not exist.

What is the exact value of sin(cos^−1(−sqrt2/2))+tan^−1(sin(π/2))?

cos^-1  (-sqrt2/2)     =   3 pi/4   (or possibly 5 pi/4 I will use the first)        sin 3pi/4  = + sqrt2/2

sin pi/2 = 1

tan^-1 (1) = pi/4

sqrt2 / 2   + pi/4     = (2 sqrt2 + pi)/4

Sorry I fixed the question is "What is the exact value of sin(cos^−1(-√2/2))+tan^−1(sin(π/2))?