Verified answer

Well!!

sec3x +√2=0 ====> sec3x = - √2

cos 3x = -1/√2

hence, 3x = cos-1 (-1/√2) = 3*pi/4

x = pi/4 = 45 degrees

sec3x = √2

3x = inverse sec of √2 (on your calculator it's sec^-1)

x = (inverse sec of √2)/3

is that sec (3x) + sqrt(2) = 0 or sec^3 (x) + sqrt(2) = 0 ??