arctan(x+y) = y^2 + pi/4 , (1,0) Use implicit differentiation to find an equation of the tangent line at the given point

First, check that the given point satisfies the equation: arctan(1 + 0) = 0 + pi/4 is true.
The slope of the tangent line is y'(x) at the given point. Differentiate the equation with respect to x:
(1 + y')/(1+(x+y)^2) = 2yy'.
Substitute x = 1 and y = 0 and obtain 1 + y' = 0, so y' = -1.
Then the equation of the tangent line is  y = -(x - 1) = -x + 1.