Attempt use of $\cos \left( {A + B} \right)$ formula to obtain an equation in $\cos \theta $ and $\sin \theta $

Use trig formula to obtain an equation in $\tan \theta $ (or $\cos \theta $, $\sin \theta $ or $\cot \theta $)

Obtain $\tan \theta  = 1/\left( {4 + \sqrt 3 } \right)$ or equivalent (or find $\cos \theta $, $\sin \theta $ or $\cot \theta $)

Obtain answer $\theta  = {9.9^ \circ }$

Obtain $\theta  = {189.9^ \circ }$, and no others in the given interval

[Ignore answers outside the given interval. Treat answers in radians as a misread (0.173, 3.31).]

[The other solution methods are $vi\alpha $ $\cos \theta  =  \pm \left( {4 + \sqrt 3 } \right)/\sqrt {\left( {1 + {{\left( {4 + \sqrt 3 } \right)}^2}} \right)} $ or

$\sin \theta  =  \pm 1/\sqrt {\left( {1 + {{\left( {4 + \sqrt 3 } \right)}^2}} \right)} $.]