Some transformations including Imagick ::rotateImage() may change "image page" -- working area inside the image you work on.

Be careful with future modifications afterwards because the image page would be different from new sizes of the image.

For example, if you do Imagic::cropImage() after rotation, you need to set image page properly, otherwise your crop would be performed relating to wrong coordinates (depending on rotation angle, resulting image size may vary).

<?php
$Image = new Imagick($sourceImagePath);

$transparent = '#00000000';
$Image->rotateImage(new \ImagickPixel(), 45); // This makes resulting image bigger

// Set page to be of the full size of new image, starting at top left corner (0, 0)
$Image->setImagePage($Image->getImageWidth(), $Image->getImageHeight(), 0, 0);

$Image->cropImage($crop_w, $crop_h, $crop_x, $crop_y);
?>

The degrees for imagick and gd is difference!
GD > rotate 90 means counter clockwise.
Imagick > rotate 90 means clockwise.

GD 90 = Imagick 270 or Imagick 90 = GD 270.

Use this function.

<?php
function calculateCounterClockwise($value)
{
    if ($value == 0 || $value == 180) {
        return $value;
    }
    if ($value < 0 || $value > 360) {
        $value = 90;
    }

    $total_degree = 360;
    $output = intval($total_degree-$value);
    return $output;
}// calculateCounterClockwise

echo '1 = '.calculateCounterClockwise(1).'<br>';
echo '90 = '.calculateCounterClockwise(90).'<br>';
echo '270 = '.calculateCounterClockwise(270).'<br>';
echo '359 = '.calculateCounterClockwise(359).'<br>';
echo '360 = '.calculateCounterClockwise(360).'<br>';
?>

test results:
1 = 359
90 = 270
270 = 90
359 = 1
360 = 0

Transparent 

<?php $im->rotateImage(new ImagickPixel('#00000000'), 75); ?>

If you want to rotate an image by a certain degree you can do this:

<?php
header('content-type: image/jpeg');
$imagick = new Imagick();
$imagick->readImage('castle.jpg');
$imagick->rotateImage(new ImagickPixel(), 90);
print $imagick->getImage();
?>