Verified Answer :

I am replacing θ with A, so don't get confused

\(csc^{2} A-4=0\)

\(csc^{2} A- 2^{2} =0\)

\((cscA+2)(cscA-2)=0\)

Using zero product property:
EITHER
\(cscA+2=0\)
\(cscA=-2\)
\(A = -30\)°

OR
\(cscA-2=0\)
\(cscA=2\)
\(A=30\)°

 


\(csec^2\beta-4=0 \\\\ (csec\beta-2)(csec\beta+2)=0 \\\\\\ \#1 \\\\ csec\beta-2=0 \\\\ csec\beta=2 \\\\ \boxed{\beta=-1.099} \\\\\\ \#2 \\\\\ csec\beta+2=0 \\\\ csec\beta=-2 \\\\ \boxed{\beta=1.099}\)