Answer
Please see below.
Work Step by Step
The function $h(\theta ) = \tan \theta +3 \theta -4$ is clearly continuous on the closed interval $[0,1]$(Please note that the points $x=\pm \frac{\pi }{2}$, at which the function is not defined, do not belong to this interval), and also we have $f(0)=-4<0$ and $f(1) \approx 0.56>0$. So by applying the Intermediate Value Theorem, there must exist some real number $c$ such that $f(c)=0$.
Looking at the graph, we can approximate the root:$$c \approx 0.9 \, .$$By zooming in repeatedly on the graph we can approximate the root much better:$$c \approx 0.91 \, .$$
Using a root calculator, we can find the root more accurately:$$c \approx 0.9071 \, .$$
