Question 1087691
Are you sure the domain of {{{theta}}} is limited to {{{ 0<= theta <= 2 }}} ?    (It looks as though it might really be {{{ 0 <= theta <= 2pi }}}  (?) )   

I ask because for {{{ 0<=theta<=2 }}}  none of the answers work because they all have values of {{{ theta}}} outside [0,2].
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If the domain is {{{ 0 <= theta <= 2pi }}} then (a) works.  

First lets factor out a {{{ cos(theta) }}}
{{{ sin(theta)cos(theta) + cos(theta) }}} 
= {{{ cos(theta)(sin(theta)+1) = 0 }}}  (*)

(*) is zero if {{{cos(theta) = 0}}} or {{{ sin(theta)+1 = 0 }}} 
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(a) 
     {{{ cos(pi/2) = 0 }}} so (*) is zero
     {{{ cos(3pi/2) = 0}}} so again (*) goes to zero.

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(b) does not work because (*) is not zero for {{{ theta = 0 }}}  or  {{{ theta = pi }}}
(c) does not work because (*) is not zero for {{{ theta = -1 }}}  ( it is zero only for {{{ theta = pi/2 }}} )