Net rotation angle of two composed 90-degree rotations

A rigid body is first rotated by $90^\circ$ about the world $z$-axis, and then rotated by $90^\circ$ about the world $x$-axis (i.e. the second rotation is applied as $R = R_x(90^\circ)\,R_z(90^\circ)$).

The composition is itself a single rotation about some axis by an angle $\theta$. Using the identity $\operatorname{tr}(R) = 1 + 2\cos\theta$, compute the net rotation angle $\theta$ in degrees.