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Is there a method to find critical numbers of a trigonometric function ?

f ( theta ) = 2 sec ( theta ) + tan ( theta )

0 <= theta < 2 pi

f ' ( theta ) = sec ( theta )  *   [ 2 tan ( theta ) + sec ( theta )  ]

set derivative to 0 to find critical numbers.

sec ( theta )  *   [ 2 tan ( theta ) + sec ( theta )  ] = 0

The only way I know how to do this problem is to plug different angle values for theta.  The values that
satisfy the equation are critical numbers.

Is there a better way to do this problem ?  Is there a method or procedure ?

This problem is from Advanced Placement High School Calculus class.
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