Answer
$\sin^2{\theta} - 4\sin{\theta} - 21$
Work Step by Step
RECALL:
$(a+b)(c+d)=ac + ad + bc + bd$ (more popularly known as the FOIL method).
Use the formula above to multiply the binomials to obtain:
$(\sin{\theta} + 3)(\sin{\theta} - 7)
\\=\sin{\theta}(\sin{\theta}) + \sin{\theta} \cdot (-7) + 3\sin{\theta}+3(-7)
\\=\sin^2{\theta}-7\sin{\theta}+3\sin{\theta} - 21
\\=\sin^2{\theta} - 4\sin{\theta} - 21$