= Solution
The central estimate is $z=3.2743$. <propagation of uncertainty> must include the occurrence of $x$ in both numerator and denominator. With angular <derivatives> measured per <radian>,
$$
z_x=\frac{\sec^2(x+y)}{\tan x}-\frac{\tan(x+y)}{\sin^2x}=-3.5382,\qquad
z_y=\frac{\sec^2(x+y)}{\tan x}=6.6497.
$$
Interpreting the two quoted errors as independent <standard deviations>, convert them to <radians> before calculating
$$
\sigma_z^2=z_x^2(4\pi/180)^2+z_y^2(3\pi/180)^2,
\qquad \boxed{z\simeq3.27\pm0.43}.
$$
If the quoted errors are instead absolute bounds, the first-order worst-case estimate is $|\delta z|\lesssim |z_x|\delta x+|z_y|\delta y=0.60$. Correlated errors add $2z_xz_y\operatorname{Cov}(x,y)$ to the <variance>. Treating $x+y$ and $x$ as independent would lose their shared <measurement uncertainty>.
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